What repercussions did Agrippina's murder have for Pompeii?

Agrippina the Younger would have exerted a powerful influence on Nero, as the woman who had secured him the throne and as the "tiger mother" who had raised and protected him amidst all the intrigues of the principate. Without her, there was no one who had any hope of checking Nero's behavior, which would eventually end in his murder, destroy his dynasty, and seriously damage his office. The authors argue that the behavior of the court would have influenced the behavior and attitudes of the public, as reflected in graffiti, artifacts, and writings found in Pompeii.

Because the figure of Nero is so hated and that of Agrippina at least controversial, the truth is hard to discern. I have not read the book being reviewed.

Agrippina Minor (or Agripinilla), Nero's mother, is one of the largest female figures of the Julio-Claudian era, not only because of her notorious son, but in her own right as a player in imperial politics.

Tacitus, Dio, and Suetonius are all rather unkind; she was a rather un-feminine (by ancient Roman standards) noblewoman close to the seat of power, and they depicted her as power-hungry, murderous, manipulative, and ruthless. But she had some support: she was, after all, the daughter of Germanicus; she was pitied for her persecution at the hands of Claudius' notorious third wife, Messalina, and she helped restore dignity as Claudius' fourth wife. Even Tacitus admits that she was upright— more or less— in describing the accession of 17-year old Nero, which really meant the state was in the hands of Agrippina:

Then came a revolution in the State, and everything was under the control of a woman, who did not, like Messalina, insult Rome by loose manners. It was a stringent, and, so to say, masculine despotism; there was sternness and generally arrogance in public, no sort of immodesty at home— unless it conduced to power. (Tac. Ann. XI.7)

But even among her defenders, it seems she was a domineering mother whom Nero came to resent. Guglielmo Ferrero, whose profile of Agrippina is so fawning it could be mistaken for satire, writes

Tacitus himself tells us that Agrippina was a most exacting mother; that is, a mother of the older Roman type—in his own words, trux et minax [fierce and threatening]. She did not follow the gentle methods of the newer education, which were gradually being introduced into the great families, and she had brought up her son in the ancient manner with the greatest simplicity.

He says of Nero's accession

There resulted in Rome a most extraordinary situation: a youth of seventeen, educated in the antique manner, and, though already married, still entirely under the tutelage of a strict mother, had been elevated to the highest position in the immense empire.… She was too intelligent not to foresee that a seventeen-year-old emperor could have no authority, and that his position would expose him to all sorts of envy and intrigue, and to open as well as secret opposition.

This, however, was a crisis which was sooner or later inevitable. Agrippina had certainly made the mistake of attempting to treat Nero the emperor too much as she had treated Nero the child…. Agrippina, though she enjoyed great prestige, had also many hidden enemies. Everybody knew that she represented in the government the old aristocratic, conservative, and economical tendency of the Claudii,—of Tiberius and of Drusus,—that she looked askance upon the development of luxurious habits, the relaxation of morals, and the increase of public and private expenditures.… Her virtues and her stand against Messalina had given her a great prestige, and the reverence which the emperor had shown for her had for a long time obliged her enemies to keep themselves hidden and to hold their peace. But this ceased to be the case after the incipient discord between her and Nero had allowed many to foresee the possibility of using Nero against her.

The expulsion of Agrippina from the palace, and then her assassination, would have thus removed the most important moderating influence on Nero, with perilous results.

The consequences that Alex Butterworth and Ray Laurence write of in Pompeii: The Living City are of challenges to the traditional social order.

Since the murder of Agrippina, Nero had pursued, ever more assidously, his own taste for activities that offended the traditional Roman sense of decorum. What had begun as an exuberantly childish reaction to the sudden lifting of all the prohibitions imposed by a strict mother— the Emperor toying first with chariot-racing, then mild debauchery, before graduating to hardcore amateur dramatics— was already degenerating into something altogether more extreme and sinister. …

Traditional Roman values such as austerity, self-discipline, simplicity, and monogamy, as well as traditional gender roles, were challenged by Nero's indulgent, impetuous, and promiscuous personal behavior, and that of his court.

With the emperor setting the moral tone for his subjects, the latter part of Nero's reign would be one of those moments in the history of imperial Rome when society's ongoing struggle between the demands of duty and delight, would bubble uncontrollably to the surface.…

... The miasmic atmosphere into which the close associates of Nero were drawn in the years that followed the murder of Agrippina: a demi-monde of unmitigated luxury, other-worldly artifice and hopeless self-delusion, where money was spent with abandon yet where the most dangerous kind of inflation was at work in the realm of desire.…

They take as evidence luxury artifacts, graffiti and signs, paintings, and of other contemporary writers such as Columella, the agricultural writer, quoted with this lament after a visit to Pompeii:

I suppose that the old-fashioned and manly way of life is no longer agreeable in the face of today's glamorous luxury.… We watch in amazement the gestures of the effeminates who are abroad, as their womanly movements imitate what nature has denied to men, and so deceive all who gaze upon them.