Strong movement to deregulate professions in the 1960's?

This is mainly part of the neo-classicist, conservative or economical liberalist backlash against mainly paternalistic or even Keynesian government interventionism.

The author of the original quote seems to allude mostly to professional bodies, like corporations (old meaning), and how they interacted with the ruling bodies (church, government, state).

The theory goes that professional associations are now confronted with impositions, under the auspices of job creation and free circulation, restraining the barriers they created to entry into the labour market. That these entry barriers were intentionally introduced as barriers to ensure quality is simply dismissed, as the ideology conscripts the "invisible hand of the free market" to sort that out.

That "strong movement" is actually not that 'strong' regarding "professions" itself. These government sanctioned, or even demanded, or imposed regulations for professsions are only a small part of a general onslaught on institutionalised regulations. But this free-market radicalism is felt in that field as well. The mantra was and still is "de-regulation is good, no matter what and where and how". Both sides of the still ongoing arguments suffer from intended and unintended consequences they both like to downplay or ignore.

While academic outcasts started to re-emphasise these ideas early on, in fact practically uninterrupted but for while without clout in face of big government advocates, they gained ground in the time frame mentioned in the quote of the question.

Deregulation 1970–2000
Deregulation gained momentum in the 1970s, influenced by research by the Chicago school of economics and the theories of George Stigler and others. The new ideas were widely embraced by both liberals and conservatives. Two leading 'think tanks' in Washington, the Brookings Institution and the American Enterprise Institute, were active in holding seminars and publishing studies advocating deregulatory initiatives throughout the 1970s and 1980s. Cornell economist Alfred E. Kahn played a central role in both theorizing and participating in the Carter Administration's efforts to deregulate transportation. The first comprehensive proposal to deregulate a major industry in the United States, transportation, originated in the Richard Nixon Administration and was forwarded to Congress in late 1971.

However, starting in the 1950s and 1960s, economic analyses of regulated industries showed more and more evidence that government regulatory policies did not seem to operate with goals of efficiency in mind, nor did they seem concerned with goals of income distribution in the traditional public-interest sense of achieving a more equitable distribution of income (Joskow and Noll, 1981, pp. 1–10).
Some students of regulated industries argued that to the extent that regulators failed to achieve traditional goals of public-interest-oriented economics, it was by accident or incompetence rather than by design.

Meanwhile, new schools of thought developed regarding motivations for public regulation -- ones which attributed self-interested rationality to regulators and to all players in the regulatory game and which tried to explain existing regulation as a rational outcome of the economic and political processes going on in the country under study, for the most part, the United States.1 Although even by the admission of some of their own authors, these theories were imperfect at predicting the existence and patterns of regulation in a given industry, they nevertheless achieved partial success in explaining patterns of regulatory policy in many industries. More specifically, many have argued that they do a much better job as a set of positive theories of regulatory behavior than the more traditional public-interest-oriented normative theories.

No sooner had these theories gained a modicum of acceptance in economics, however, than a strange thing happened: during the mid-to late 1970s, Congress, the White House, and the regulatory agencies all worked together toward a set of dramatic regulatory reforms, first in airlines, then in railroads, and finally in trucking, all dramatically loosening government controls on these industries, and with public-interest concerns and the advice of academics an important influence in the process. In other words, no sooner had revisionist theories of regulation gained acceptance than we got reforms contradicting these revisionist theories. Other, similar reforms, both loosening regulation and claiming to represent the best economic interests of the United States public, have been instituted or are underway in telecommunications, banking, other financial institutions, petroleum extraction and sales, and natural gas extraction. Yet other industries, such as international maritime and air transportation, agriculture, and environmental and safety concerns, seem as regulated as ever.
_{Theodore E. Keeler: "Theories of Regulation and the Deregulation Movement", Public Choice, Vol. 44, No. 1, Carnegie Papers on Political Economy, Volume 4: Proceedings of the Carnegie Conference on Political Economy (1984), pp. 103–145. (jstor)}

Deregulation Pros, Cons, and Examples –– Why Airline Travel Is So Miserable, and Other Effects of Deregulation

The de-licensing of occupations in the United States (2015)

Although it's from a European perspective, the initiators of this 'movement' are influential internationally: Raquel Rego (Eds.): "The Trend towards the European Deregulation of Professions and Its Impact on Portugal under Crisis", PalgraveMacmillan, 2013. (gbooks)

Running with the example of the legal professsion in America:

Unfortunately, the second half of Let's Deregulate's argument suffers from gross over-reach. It is one thing to extrapolate from demonstrably true propositions, for example, the requirements for entering the legal profession are very expensive or that more people would like to enter the legal profession than are allowed to (limiting the supply of legal services and increasing the cost). It is a different matter to argue that lawyers have successfully lobbied for complex regulations in an effort to drive up their salaries. The causes, costs, and benefits of environmental regulation are too varied and complicated to boil down to just their effect on the legal profession. Moreover, the idea that lawyers are the prime movers behind these regulations is, to put it kindly, a challenging empirical proposition.
_{Benjamin H. Barton: "Economists on Deregulation of the American Legal Profession: Praise and Critique", Michigan State Law Review Vol. 2012:493}

Or perhaps

In the modern world, it is also true that associational self-regulation constitutes markets. The self-regulation of stock exchanges (associations of brokers) constitutes this most central institution of the capitalist economy (Stenning et al., 1987);3 the self-regulation of the legal (Halliday, 1987) and accountancy (Willmott, 1985) professions is vital to constituting the legal and accounting framework without which markets would collapse into disorder.

Earlier we pointed to the importance of professional self-regulation in constituting markets. An example of the countercurrents in an era of regulatory flux is that one of the authors finds himself in the early 1990s involved as a part-time Commissioner with the Australian Trade Practices Commission (TPC)4 to urge self-deregulation on some professions. This means, for example, urging the professions to dismantle restrictions on advertising, fee setting, and barriers to entry so that markets for professional services might become more competitive. Should the appeals for self- deregulation fail, perhaps a more litigious state-enforced deregulation (regulated deregulation!) will ensue.

Regulatory actors also have multiple selves: they can be nice guys or tough guys, self-interested or public-spirited, professional or unprofessional, diligent or lazy, intelligent or confused. The stuff of regulatory disasters is where the tough, unprofessional, confused self of the regulator encounters the irresponsible profit-driven self of the business executive. Such disasters come to everyone's attention— the head of the regulatory agency cops flak from them, the industry association publicizes them as evidence of the unreasonableness of regulatory demands, the public interest group publicizes them as evidence of industry rapaciousness and irresponsibility, and scholars write books about them.
_{Ian Ayres & John Braithwaite: "Responsive Regulation: Transcending the Deregulation Debate" (Oxford Socio-Legal Studies), Oxford University Press: Oxford, New York, 1992. (online: PDF, Review.)}

The ongoing debate is illustrated by ongoing propaganda, in this case peppered with some history of that debate:

Lawyers are among the 20 percent of the U.S. labor force that is required to obtain a government license to practice a profession (Kleiner 2006)—a requirement that may not be justified, as suggested by the preceding anecdotes, because some legal services could be competently provided by persons who have not had a formal legal education and who have not passed a state bar examination to obtain a license. Even people who do have a legal education are prevented from taking a bar examination and practicing law in all but a few states unless they graduated from an ABA-accredited law school. And ABA regulations prevent licensed lawyers who work for firms that are not owned and managed by lawyers from providing legal services to parties outside their firm. The ABA-imposed entry barriers are one important factor that we argue unnecessarily raises the cost of legal services. Before discussing the other important factor—that lawyers have become an effective interest group—we summarize how the ABA came to exert such a powerful influence on the practice of law.

The Evolution of the ABA’s Influence
The association first attempted to include its accreditation of law schools as part of states’ occupational licensing of lawyers in 1921, when, claiming concern over the quality of the legal education being administered, it adopted a statement of minimum standards of legal education and instituted a policy of publishing a list of law schools that complied with those standards. Whether this policy had beneficial effects and was justified is unclear: it is difficult not only to measure the quality of the legal education at the time but to verify that the ABA’s accreditation standards improved it. Some commentators argue that the true motivation for the standards was to prevent minorities and the poor from joining the profession (Auerbach 1971). If true, that motivation would undermine an alleged benefit of occupational licensing: that it can increase the presence of minority workers by serving as an imprimatur of worker quality.

Initially, state legislatures were not persuaded by the ABA’s alleged justification for its standards, and four years after the standards were developed, not a single state required graduation from an ABA-accredited law school for admission to the bar. But by the 1950s the U.S. Department of Health, Education, and Welfare had recognized the Council of the ABA Section of Legal Education and Admissions to the Bar as the sole accrediting agency for degree-granting law schools, and about half the states had education requirements based on ABA standards. Friedman (1962, p. 153) suggested that the other states did not have such requirements because many state legislators themselves were graduates of unaccredited schools: “If they voted to restrict admission to the profession to graduates of approved schools, in effect they would be voting that they themselves were not qualified.” Friedman later predicted that as more legislators were trained at accredited law schools, the ABA standards would be more broadly accepted (Fossum 1978). Indeed, Friedman’s forecast has proved to be correct: today, all but a few states, notably California, require would-be lawyers to have graduated from an ABA-accredited law school, and every state except Wisconsin requires them to pass a bar exam.
_{Clifford Winston & Robert W. Crandall & Vikram Maheshri: "The First Thing We Do, Let's Deregulate All The Lawyers", Brookings Institution, Washington, 2011. (also: a lecture)}

An overview of the changes – that is in regulation, deregulation and re-regulation – for medical, legal and accounting professions in the US, but largely disregarding the economic side and focusing on ethics:

Each of the professions experienced an "expectation gap" in the post World War II era. The physicians in the 1950s when the public, armed for the first time with widespread health insurance, held high expectations for the growing specialization and high technology in medicine. The lawyers in the 1960s when they were blamed for the failure of the •U.S.justice system to provide equal opportunity for all. The accountants in the 1970s due to the financial failure of organizations who had just received a "clean" audit opinion. Each profession sought a partial solution in a revised code of ethics. The changes within society prompted changes within the professions.
Lastly, the legal profession experienced significant changes within the profession in the 1970s and 1980s. The number of lawyers and the type of law they practiced changed drastically. The "new" lawyers had an impact on the codes that were adopted in 1969 and 1983. The growth of specialization in medicine does not seem to have had a significant impact on the AMA code adopted in 1980. The accounting profession has seen a growth in the number of CPAs working outside public acounting. While the 1988 code affects them, the CPAs in private industry did not significantly influence the writing of the Code.

Members of the legal, medical and accounting professions are guided by their respective codes of ethics. The professions created and changed their codes of ethics for various reasons. As the professions grew and developed, changes within the professions prompted changes in the codes. Additionally, events outside the profession, such as economic and social change and governmental influence, often prompted changes in the codes of ethics. Sometimes two or more professions were affected by the same event, as in the changing social and economic conditions in the early 20th century and the governmentad influence on advertising rules in the 1970s. Often, all three professions seemed to lack the foresight to make changes in their codes before governmental action or other outside pressure forced the change.
_{Jeanne F. Backof & Charles L. Martin,Jr.: "Historical Perspectives: Development of the Codes of Ethics in the Legal, Medical and Accounting Professions", Journal of Business Ethics 10:99–110, 1991.}

From a historical-sociological perspective, covering US, UK and Canada:

The two most common are Neo-Weberian and Foucauldian (Chamberlain 2013; Saks 2015). According to Neo-Weberian social closure theory, professional regulation in Anglo-American contexts was the product of campaigns by (male) professionals who organized, and mobilized economic, social, and cultural resources to lobby governments for regulatory privileges (Macdonald 1995; Larson 2013; Saks 2015). Self-regulating professions have successfully enacted social closure, cutting off others’ access to education, credentials, and opportunities to practice, and they reap the rewards of their privileged position. Although Neo-Weberian scholars acknowledge that professionals’ ability to enact social closure is bolstered by the authority of the state, they tend to under-theorize profession–state relations. In these accounts, state actors simply grant powers to professions upon request. Professional groups have struck a ‘regulatory bargain’ with the state: professions were historically granted autonomy and regulatory powers in exchange for their promise to use these powers responsibly and in the public interest (Macdonald 1995; Flood 2011; Gorman 2014). According to this view, state actors seek only the protection of the public through professional regulation; they have no goals or interests of their own. Traditionally, the public was said to benefit from professional regulation because it raised service quality, and informed consumers which service providers were most qualified (Law and Kim 2005; Kleiner 2006).
In contrast, Foucauldian accounts portray the state as much more active in profession creation, arguing that the establishment of self-regulating professions was historically a component of state-building, and the expansion of the state’s capacity to govern (Johnson 1993, 1995). Self-regulating professions are semi-autonomous governance institutions that extend governmentality. From this perspective, a different—and often ignored—regulatory bargain is revealed: in return for regulatory powers and authority, professions benefit the state by extending governance in certain social areas (health, justice, finance), without drawing heavily on state resources. Most self-regulating professions are self-financing: it is the regulated professionals themselves who fund the regulatory body that governs them (Jordan and Richardson 1984; Stacey 1995: 67). This regulatory bargain may have been particularly appealing to state actors in the nineteenth century, when the size of state infrastructures—especially in new countries and colonies like the USA and Canada—was quite small. Over time, the state extended its reach, ‘in partnership’ with elites and groups including professions, who shared its concern with control (Dent 1993; Larkin 1995: 26; Chamberlain 2013).
Abbott’s (2005) linked ecologies perspective provides another way of theorizing professional regulation and state–profession relations. For Abbott, the state and professions are linked ecologies: ‘complex interactional structures’ composed of actors, locations, and the linkages or relations between them (Abbott 2005: 247–8). To understand regulatory outcomes, Abbott argues, we need to understand how these two ecologies interact and intersect.
Professional regulation is a product of developments in both the professions and state ecologies; regulation may be more likely to occur when it serves actors in each ecology. Abbott’s (2005) linked ecologies perspective provides some middle ground between a neo-Weberian approach that casts the state as passive and responsive to professions’ demands, and a Foucauldian approach which focuses on governmentality to the neglect of other interests and concerns that might shape state actor activity and regulatory outcomes. To understand regulatory change and outcomes, according to Abbott, we should focus on both state actor and professional interests and concerns, and consider when and how these interests intersect.

Quebec’s regulatory change was longer lasting, and more sweeping as it affected not only health professions, but every profession in the province. Quebec’s Commission of Inquiry on Health and Social Welfare concluded that professions should be intermediaries between the state and the public (CNC 1970). The state had failed in its duty, delegating too much of its own power to professional corporations (CNC 1970: 24). This had resulted in a chaotic system, rife with discrimination, elitism, interprofessional conflict, and inflexibility.
_{Tracey L. Adams: "Self-regulating professions: past, present, future", Journal of Professions and Organization, 2017, 4, 70–87, doi: 10.1093/jpo/jow004}

These quite practical but unintended and unwelcomed outcomes for the professions mentioned in the question

Everywhere in the United States the professions have reached new heights of social power and prestige. Everywhere, because of the power of their special knowledge, they are of increasing consequence in the lives of individuals and in the affairs of groups, the polity, and the society as a whole. Yet everywhere they are also in trouble, criticized for their selfishness, their public irresponsiblity, their lack of effective self-control, and for their resistance to requests for more lay participation in the vital decisions professionals make affecting laymen.
The signs of this trouble are manifest in many quarters. In California the governor has for the first time appointed laymen to every one of the state boards that regulate professional conduct; formerly these boards were monopolized and dominated, run in their own interests, by the professionals themselves. In New York State the legislature has passed new laws requiring more effective peer control over delinquent medical practitioners. Also in New York, The Board of Regents, which has responsibility for the public control of some twenty-nine "professions," has recently voted to permit professions to do limited advertising in newspapers and magazines. Further, it has issued a new regulation requiring health professionals to show a patient his medical records upon request, except when this "would adversely affect the patient's health." This latter exception is an application of the therapeutic privilege, which sets certain limits on the patient's right to know, the doctor's duty to tell. In 1973 the U.S. Congress established the National Commission for the Protection of the Subjects of Bio-medical and Behavioral Research to reduce long-standing abuses against the persons and civil rights of the subjects of biomedical and social research. In 1974 a report on medical malpractice was issued by a commission appointed by the secretary of the Department of Health, Education, and Welfare. As the problem of medical malpractice continued to become more severe, the State of New York appointed its own investigatory panel which issued its report in 1976. In the same year, another Senate committee, the Committee on Government Operations, investigated the malfeasance of another powerful profession, the accounting profession. The "arrogance" and "elitism" of the academic profession, which trains and sets standards of self-control and responsibility for the other professions, have also recently been criticized. So widespread and recurrent is public protest against the irresponsible power of the professions that two sociologists have referred to "the revolt of the client" as a now endemic phenomenon in American society.

Complaints about defects in public service performance and in effective self-regulation reach a crescendo in the case of the legal profession. Writing a scholarly history of the American legal profession from 1890 to the present, Jerold S. Auerbach entitles his book, Unequal Justice. "In the United States," he says, "justice has been distributed according to race, ethnicity, and wealth, rather than need. This is not equal justice." Nor has this injustice been the fault of the less well trained among the lawyers, the "less professional" members of the bar. 'The professional elite," continues Auerbach, "bears a special responsibility for this maldistribution. Its members, absorbed with selective client-caretaking for a restricted clientele, have preserved social and economic inequality. Their efforts, in conjunction with the limitations of an adversary process largely dependent upon the ability to pay, have crippled the capacity of the legal profession to provide equal justice under law or to fulfill those paramount public responsibilities that alone can justify professional independence and self-regulating autonomy." Because his evidence shows in detail that the legal profession does not serve the community as a whole but the interest only of one part – the affluent, the powerful, and the ethnically and racially privileged – Auerbach concludes his book with an eloquent call for more public control and regulation. Auerbach's findings and conclusion are supported by a study of "the unseen power of Washington lawyers," a study that calls these lawyers who sit so close to the national seats of power "the other government."24 'The bar," Time magazine quotes Professor Vern Countryman of the Harvard Law School as saying on the eve of the one hundredth annual meeting of the American Bar Association, "is still dominated by shortsightedness and self-interest.

The public is not radically anti-intellectual or anti-scientist, as some academics fear, but it is ambivalent about the mixed consequences of academic professionalism and it is, increasingly, demanding more lay and democratic control over some of these consequences. Academic professionals who resent or resist an increased measure of public control may well take note of Duncan Macrae's remark: "Democracy, however, requires that the electorate have the ultimate power. Those who value democracy, or fear its erosion, sometimes see scientists as an elite serving special interests, or see science as simply unplanned and uncontrolled."
_{Bernard Barber: "Control and Responsibility in the Powerful Professions", Political Science Quarterly, Vol. 93, No. 4 (Winter, 1978–1979), pp. 599-615, (jstor).}