Kant, a Protestant, although not mentioning the Summa by name, harshly criticized its arguments—e.g., he does not believe cosmological arguments, such as what St. Thomas used to prove God's existence, are valid. Kant also criticized the medieval "Schools" that were associated with Thomism. See this quote from Kant's Critique of Pure Reason regarding the "Monopoly of the Schools".

The Summa threatens even 20^th century Freemasonry, many of whom are Protestants:

The difficulties between Church and State in Italy had culminated seven years before in the nomination of Crispi, a man wholly hostile to the Church [and a friend of Garibaldi, another Freemason], as Prime Minister. On the eve of the elections in 1890 his friend Semmi, like himself a Freemason and Grand Master of the Italian lodges, had spoken strongly on the necessity of destroying the Great Enemy [i.e., the Catholic Church]. "We have applied the knife to the centre of superstition," he wrote in a wonderful combination of mixed metaphors, "and the very presence of ***** at the head of Government is a guarantee that the Vatican will fall beneath the blows of our vivifying hammer. Let us work with all our strength to scatter its stones, that we may build with them a temple to an emancipated nation. The enemy is the Pope; we must wage a relentless war against him. The Papacy, although but a phantom presiding over ruins, yet reflects a certain glory, waving as it does in face of, and in defiance of the world, the Cross and the Summa Theologica. A miserable crowd still prostrates itself to adore. It must be war to the knife."

—The Life of Pius X by F. A. Forbes, imprimatur 1918, pp. 45-46 (my emphasis)

I found what maybe the perfect journal article that addresses your question: McNeill, John T. “Natural Law in the Teaching of the Reformers.” The Journal of Religion, vol. 26, no. 3, 1946, pp. 168–182. A copy can be found at JSTOR. Its 15 pages are divided into 4 sections treating Luther, Melanchthon, Zwingli, and Calvin individually.

I believe the Reformers's issue with Aquinas and the scholastic theologians in general, is about natural theology, not natural law, since the Reformers believed that the Medieval approach to Christian theology was too much influenced by Aristotle that the scriptural interpretation has been compromised. This is part of the larger humanistic enterprise which called for Ad fontes ("to the sources") not only to classical Latin (for humanists like Erasmus) but also for the Reformers going back to the Hebrew and Greek manuscripts as opposed to relying on the Latin translation for the Bible.

I share the observation of the OP and lament the fact that Protestants rarely use Natural Law reasoning when it comes to defining their Christian position on controversial ethical topics of today. While the article doesn't directly treat why this happened, many citations of the Reformers's writing on their understanding of natural law may point to the Reformers's distrust on using reason for moral argument since they believed reason itself has been compromised by sin. Thus they severely restricted the application of natural law reasoning to minor duties, one of which was to explain why pagans could behave justly even without revelation (answer: because even after the Fall there are still traces of natural law which is implanted by God into human hearts). This then forced them to rely more on scriptural arguments. I'm sure they couldn't have anticipated how Bible authority has been severely diminished 500 years later, and Christians need all the help they can from Christian and non-Christian philosophers alike who still cling to the belief of objective morality, just like how Plato and Aristotle reacted very severely to the Sophists who deny that there is an objective basis of morality.

As another poster already pointed out, the Reformers didn't mention Summa Theologica in their writings, so the article also doesn't mention the Reformers's position on the Summa. Again, I lament that Protestants don't make use of the excellent treatment of virtues, vices, and human nature in the Summa. It looks like the trend has started all the way since the Reformers's own period, and maybe due to the SAME distrust of Aristotle I mentioned above. The critical element of Aquinas's theory of virtues is Aristotle's Final Cause, but with the pre-modern scientists ALREADY reacted negatively to Aristotle's Final Cause, probably the Reformers were loath to use Final Cause in the areas of moral reasoning as well, although now Final Cause even in the area of science is beginning to make a comeback. Without Final Cause, it is no wonder that the Reformers wouldn't use natural law argument either because Final Cause is the most important element of natural law argument. In the modern period, natural law begun to be redefined beyond recognition since the Final Cause element was thrown out, which reduces today's applicability even more. If we were to bring back natural law argument, we will need to restore respectability to the Final Cause element FIRST. Excellent treatment of the historical development of natural law can be found in the Teaching Company's Great Course on "Natural Law and Human Nature"

Below is the first paragraph of the article:

THERE is no real discontinuity between the teaching of the Reformers and that of their predecessors with respect to natural law. Not one of the leaders of the Reformation assails the principle. Instead, with the possible exception of Zwingli, they all on occasion express a quite ungrudging respect for the moral law naturally implanted in the human heart and seek to inculcate this attitude in their readers. Natural law is not one of the issues on which they bring the Scholastics under criticism. With safeguards of their primary doctrines but without conscious resistance on their part, natural law enters into the framework of their thought and is an assumption of their political and social teaching. This is assuredly not a consequence of what we may all the" active" element of their theology, which denies independent value to good works in the realm of salvation and throws into relief man's sin and God's supernatural grace. The seeming incongruity here is not our present problem. The assumption of some contemporary theologians that natural law has no place in the company of Reformation theology cannot be allowed to govern historical inquiry or to lead us to ignore, minimize, or evacuate of reality, the positive utterances on natural law scattered through the works of the Reformers. The bearing of natural law upon theology in these writings still calls for clarification. In this study we must observe a rigid economy, which excludes all that is peripheral to our special topic and, therewith, much that is important for the history of theology. But reference to some points in the area of contact is unavoidable.

Luther

According to

• Steinmetz, David Curtis. 2002. Luther in Context. Grand Rapids, Mich: Baker Academic.,

Luther had no direct knowledge of the content St. Thomas Aquinas's Summa Theologica. Luther in Context ch. 5, "Luther Among the Anti-Thomists," begins:

Did Luther know the theology of Thomas Aquinas? Historians, particularly Roman Catholic historians, have raised serious questions about Luther's familiarity with the theological positions of St. Thomas. Joseph Lortz, for example, suggested that the tragedy of the Reformation was traceable in part to Luther's ignorance of the balanced synthesis of grace and free will in Thomas's theology. Luther lived in a time of theological unclarity, dominated by the "fundamentally uncatholic" theology of William Ockham and his disciples. Luther made a legitimate Catholic protest against the uncatholic theology of Ockham and Biel, only to press his point too far and fall into doctrinal error. Had Luther only known the Augustinian theology of Thomas Aquinas, argued Lortz, he would have found adequate Catholic resources to combat the decadent theology of the Occamists without lapsing into heresy.

However, Luther did burn St. Thomas Aquinas's works, including the Summa Theologica, on 10 December 1520, along with Pope Leo X's bull Exurge Domine that condemned his errors and excommunicated him. From Facts about Luther ch. 3:

Luther followed up this imprecation and invective on Rome [i.e., his Against the Execrable Bull of Antichrist] by publicly burning on the 10^th day of December, 1520, at the eastern gate of Wittenberg, opposite the Church of the Holy Cross, in the presence of many students, who jeered and sang ribald drinking songs, the Bull of Leo X and all his writings, together with the works of St. Thomas Aquinas and other Catholic theologians. On the day after this contemptuous exhibition, Luther preached to the people and said [in his sermon Why the Books of the Pope And His Disciples Were Burned of LW 31]:

Yesterday I burned in the public square the devilish works of the Pope; and I wish that it was the Pope, that is, the Papal See, that was consumed. If you do not separate from Rome, there is no salvation for your souls.

Calvin

I quote this answer to the Christianity StackExchange question "Did John Calvin ever read Thomas Aquinas's Summa Theologica?:"

A smoking gun is in the references that John Calvin makes to Thomas Aquinas in his own book, The Institutes of the Christian Religion (II.11.4 and III.22.9). This is evidence that Calvin at least knew of Aquinas, which suggests that Aquinas' most important work had reached France or Switzerland and that he would probably have read it.

Mark J. Larson says in Calvin's Doctrine of the State, page 27, that Calvin read Aquinas either directly or through intermediate sources (citing Lane and Wendel as his own sources). Larson says that although Calvin did not explicitly connect his teaching on the just war with Aquinas, it could well be the case that he had read his treatment De Bello in Summa Theologica.

James Dolezol, a recent doctoral graduate of Westminster Seminary in Philadelphia, has written a book (which was his dissertation) on divine simplicity in which he traces the agreement of Reformed scholasticism to Thomist scholasticism on the doctrine of God. I have not yet read this book, but I was told about it by a friend of Dolezol's, and I listened to an interview of him about it on Christ the Center. He demonstrates that the Reformed scholastics fundamentally agree with Aquinas on doctrine of God (and the Summa Theologica is of course a major work in the development of Aquinas' theology proper—it is the first subject he broaches). My friend who knows Dolezol and is himself a graduate of Westminster and well-read, told me that Aquinas was John Owen's favorite theologian (an assertion which I find astonishing and difficult to believe). Owen is considered by some Reformed scholars to be the foremost Puritan theologian, and the greatest theologian since Calvin up to his time.

Thus the Reformers did not simply throw out the Summma Theologica. I am, however, unversed on their respective positions on natural law, which @gmoothart has addressed briefly in his answer. Francis Schaeffer faults Thomas in How Shall We Then Live? and Escape from Reason for his epistemic nature/grace dichotomy, which is the basis of the Thomist conception of natural law. I believe that Schaeffer does this on the basis of his faithfulness to classic Reformed theology. Nevertheless, that is not a direct answer with regard to the original Reformer's position on Aquinas' natural law doctrine. Dolezol and Owen may be a good starting point for a further investigation of the question.

I can only speak for Calvin. AFAIK, he never explicitly interacts with Aquinas or the Summa. In Institutes he does reference "The Schoolmen" many times, but he seems to have in mind mostly later-medieval theologians rather than the angelic doctor himself. That's a shame, because Aquinas would have been a much more worthy opponent.

Protestants in general tend to be skeptical of natural-law arguments. Calvin himself believed that our only reliable knowledge about God comes from special revelation and he is very hard on the "Papists" for making stuff up (i.e., the incredible detail some writers claim to know about the kinds and hierarchies of the angels).

That said, I believe Calvin would have come down on the same side as the Catholic Church on the issues you mentioned. He certainly would have opposed contraception.

Edit

Here are a few google results, suggesting that Calvin probably did not have access to the Summa:

Calvin on Aquinas

Luther, Calvin and Aquinas: On Grace