That, and other attributes, made the Quakers a good faith candidate for "pet religion" of that era. The Quakers were Protestants who just preceded the Enlightenment. But during the period of that era, the leading thinkers sympathized with the Quaker thought and theology they discovered.
The Quakers stressed "the light." The age about which we speak was "the Enlightenment." Perhaps the words took on a slightly different meaning, but the terms "fit." (Sources for Quakers and "the light" abound online if one wants to learn more on their understanding.)
One might wonder why more men who appreciated Quaker theology didn't convert. An interesting social dynamic of that era was America's Founders tended to remain formally and nominally affiliated with the sects in which they were raised for social purposes. But often didn't believe in the official doctrines or creeds of those churches.
The Quakers' stance on pacifism meant they couldn't support the Whigs' war against the Tories. This was an obvious roadblock to American Whigs' full endorsement of Quakerism. Hence, John Dickinson and William Livingston would arguably qualify as "half-Quakers" a term Livingston used to describe himself.
Here is an article published by a George Fox University's Quaker Studies which documents the history of Voltaire's thoughts on the Quakers which terminated in "outright admiration."
Here is from the legendary Alan Charles Kors writing in The American Interest on "Voltaire's England."A taste:
Voltaire opened his Lettres with a survey of English religion, beginning with the Quakers, which, for his French audience, would have been the rough equivalent today of beginning a survey of the United States with the Reverend Sun Myung Moon’s Unification Church or the Hare Krishna movement. He lavished praise upon the Quakers’ commitment to religious tolerance, both in England and, more dramatically, in Pennsylvania, where they had political power. Foremost among the “wise laws” promulgated by William Penn had been “to harm no one for his religion.” Voltaire concluded his discussion of English religion with an account of the tolerant Unitarians, equally mysterious and heretical for his French readers.Finally, here is from a presentation given by Marie-Jeanne Rossignol, Professor of American Civilization, Dean for Education and Programs, University Paris 7 on "The Atlantic Enlightenment, in France and the United States, at the time of the War of Independence and the Peace of Paris."
Between the letters on the Quakers and Unitarians, Voltaire described the Anglican and Presbyterian establishments. For Voltaire, the Church of England itself, though an established church beset by corruptions that looked large in England (but very small indeed in France), had abandoned its efforts to coerce religious belief. In Voltaire’s view, “An Englishman, as a free man, goes to heaven by whatever path he chooses.” True, the Presbyterian Church, heir to the Calvinism that, Voltaire believed, had prevailed in the darkest times of the 17th century, possessed a clergy that detested all dissent. It was true, also, that the Episcopalian and Presbyterian clergies loathed each other, but in England the people themselves were weary of religious hatreds and persecutions, which mattered more.
Yet American society came gradually to be seen as some kind of enlightened utopia before, during, and immediately after the War of Independence. As I suggested earlier, Quaker Pennsylvania had long appeared as a heaven of simplicity and democratic manners, as opposed to aristocratic France. Voltaire spread this idea, which gained more currency at the time of the War of Independence: in the 1780s a large body of literature was devoted to the New World, and the new nation in particular. Many French travelers to the United States contributed to this literature. In France but also in the rest of Europe, Britain gave way to the United States as a modern political model. Now the French no longer wanted to flee to London to avoid censorship: they dreamt of moving to the United States. A case in point is Jacques-Pierre Brissot, a future revolutionary leader in 1792-1793. He had been fascinated by Britain in the 1780s and repaired to London to avoid political problems in France: there he met with radicals but also with enlightened mainstream political figures such as Lord Mansfield, the Chief Justice. He also met with Quakers, then at the forefront of the antislavery fight, and under the influence of famous American Quakers such as Anthony Bénézet.
By 1786, Brissot had been converted to the cause of America, like many French philosophers and journalists. To be enlightened was to be free ( the words light, enlightened and enlightened are to be found obsessively under his pen, as well as free and freedom) and to be free was to be in the United States. Beyond enjoying the kind of liberal institutions enlightened thinkers were hoping for, the United States also made it possible to consider economic prosperity for such lower-middle class publicists as Brissot through its cheap access to land. ...