Time once again to revisit "The Synthesis" of ideologies that was the American Founding. The vast majority of expert scholars of whatever ideological background agree with Harvard's Bernard Bailyn that the American Founding synthesized Greco-Roman, Judeo-Christian (biblical), Common Law, Whig, and Enlightenment. There is debate as to whether these disparate strands are compatible with one another. But in the minds of the American Founders, they were. To the extent that they may not have been, the Founders, using their reason, made them "fit" even if they had to "revise" to achieve those results.
This quotation of Jefferson on Christianity comes to mind:
"Were I to be the founder of a new sect, I would call them Apiarians, and, after the example of the bee, advise them to extract the honey of every sect."
-- To Thomas B. Parker, May 15, 1819.
When it came to "religion" a great deal of what these "rational Christians" believed in or admired, was already dispersed throughout Christendom. Indeed, they tended to have an affinity for the "primitive Christianity" of the earliest era before it got corrupted by Trinitarian creedalism. Doctrines for which they tended to have affinities like Arianism, Socinianism, Universalism predated the Enlightenment.
But during the Enlightenment, it all started to come together. For instance, we have noted, on resisting tyrannical government, Calvinists (though not Calvin himself) and before them medieval scholastics, argued something similar to the Lockean Enlightenment theories of resistance which America's Founders adopted.
But, while I can't speak for medieval scholastics whose views on the matter I need further to research, I do know that on religious liberty -- what America's Founders thought the most unalienable of rights -- the Calvinists, including the "resisters" were horrible, as bad as Calvin himself.
This is what Samuel Rutherford said of Roger Williams' emerging views of liberty of conscience:
"It was justice, not cruelty, yea mercy to the Church of God, to take away the life of Servetus, who used such spirituall and diabolick cruelty to many thousand soules, whom he did pervert, and by his Booke, does yet lead into perdition."—Samuel Rutherfurd, A Free Disputation Against Pretended Liberty of Conscience. (1649).
Yet, Roger Williams and the Quakers did innovate on ideas of religious liberty and separation of church and state. And they were not at all in the tradition of Calvinist Christianity. (Williams at one point seemed to be a Calvinist, but quickly moved towards a unique religious sect unto himself). I have no idea how Roger Williams and the Quakers theorized, in principle on how to deal with tyrannical magistrates. Though in practice it was, if you don't want to be civilly punished, get the f--k out of our territory and found your own colony, which they did.
Locke seemed to have most of what America's Founders were looking for on both the issues of resistance and religious liberty; though America's Founders self-consciously extended religious liberty further than Locke did.
But those pre-Lockean sources that had what America's Founders were looking for, had only bits and pieces. Arianism here; Socinianism there. Universalism here; natural law there. Resisting the magistrate here; religious liberty and separation of church and state there.
The Founders operated as Apiarians, to use Jefferson's term, took from the various sects what they found useful and put it all together into a whole package during their Enlightenment times.