Short answer:

That's not exactly wrong, but it isn't quite right either

Discussion:

It sounds like a rather mangled gloss on an important book -- Lynn Hunt's "The Family Romance of the French Revolution" and the many books of Robert Darnton, particularly "The Literary Underground of the Old Regime".

Hunt and Darnton have more subtle arguments. There was a growing bourgeoisie and reading class. Publishers satisfied the public's appetite for lurid tales, and this became damaging to the prestige and legitimacy of the monarchy, particularly in the celebrated "Diamond Necklace Affair". This was a complicated story, in which Marie Antoinette was actually blameless, but she became tabloid fodder.

The monarchy had been hitherto something very distant from the people, but the publications of the day portray them in an increasingly graphic and demeaning fashion, going some way to stoking a hatred. It's important to distinguish the nobility from the monarchy-- they're not at all the same thing. Substantial parts of the nobility were in favor of limiting the powers of the King (notably the power to tax), and the early days of the Revolution are _not_ a "people vs nobles" uprising, though that becomes the tenor of the battle after the death of Mirabeau and with the coming of the Terror.

So it's important to think about publications in two distinct phases:

1. Pre-revolutionary publications which somewhat diminished the respect in which the monarchy was held
2. Publications _during_ the course of the Revolution -- eg after 1789-- which stoked hatred for the the monarchy, particularly the Queen. Quite a few of these publications are obscene, depicting Marie Antoinette in a notably vulgar fashion (the King figures much less in these).

So far as pornography and the Revolution go, there's a complicated story for the literary critics. Starting with the remarkably popular novel Therese Philosophe (1748) and continuing through the works of Restif de la Brettonne and the Marquis de Sade, the French took their literary pornography seriously. Its hard to say that these works mattered to the sans-culottes -- their intended and actual audience wasn't the crowd that stormed the Bastille.

A more nuanced reading is that the 18th century was a time when the legitimacy of old prejudices and customs was being eroded. For the hedonist there was libertinism. In a more serious vein, there was Republicanism, Freemasonry and constitutional monarchy. So I'd push back on the notion that "porn helped start the French Revolution" and suggest rather that libertinism, populism and hostility to established authorities -- whether Kings or Churches-- were all manifestations the same Enlightenment values, results rather than causes. Those hostile to the Revolution tended to exaggerate the significance of sexual license; equating libertinism to liberalism perhaps. And Edmund Burke can draw a line between scurrilous publications and Revolution; he has a good word for the Bastille when condemning Madame de la Motte, Marie Antoinette's antagonist in the Necklace Affair, who'd fled to London

We have prisons almost as strong as the Bastile, for those who dare to libel the queens of France. In this spiritual retreat, let the noble libeller remain

The contemporary reviewers of Therese Philosophe denounced it as "materialist", "deist", "fatalist" and "spinozaist" (referring here to the Jewish philosopher Baruch Spinoza). That's a lot of heavy condemnation for a book that looks to us fairly trivial-- but if the contemporary readers saw more importance in this seemingly slight book than we might, we should listen to them. The danger that these works created was arguably not so much to "challenge the respect and reverence commoners were supposed to give", but more to erode the seriousness with which elites took the duties of their station.

Sources:

Ivker, Barry. “John Cleland and the Marquis D'Argens: Eroticism and Natural Morality in Mid-Eighteenth Century English and French Fiction.” Mosaic: A Journal for the Interdisciplinary Study of Literature, vol. 8, no. 2, 1975, pp. 141–148.

Lynn Hunt, "The Family Romance of the French Revolution" (University of California Press:1992)

Robert Darnton "The Literary Underground of the Old Regime" (Harvard University Press:1982)

McCalman, Iain. “Mad Lord George and Madame La Motte: Riot and Sexuality in the Genesis of Burke's Reflections on the Revolution in France.” Journal of British Studies, vol. 35, no. 3, 1996, pp. 343–367.

Annie DUPRAT, Marie-Antoinette (1755 1793) : images et visages d'une reine, Paris, Autrement, 2013

DUFLO, COLAS. “Aspects Philosophiques Du Roman Libertin: Thérèse Philosophe.” Archives De Philosophie, vol. 78, no. 3, 2015, pp. 433–450