My research has moderately explored America's Founders' strong affinity for noble pagan Greco-Roman antiquity. And this in turn was part of their Whig-Enlightenment worldview. I've noted how Washington's hero was a figure from antiquity named Cato the Younger who committed suicide as a matter of principle rather than submit to the tyranny of Caesar. The authors of the Federalist Papers adopted the surname "Publius." And Washington (and some of his soldiers and intimates) were affiliated the Society of Cincinnati named after the pagan figure LUCIUS QUINTIUS CINCINNATUS. This is from their 1783 founding order:
Tuesday, 13th May, 1783
The representatives of the American Army being assembled agreeably to adjournment, the plan for establishing a Society, whereof the officers of the American Army are to be Members, is accepted, and is as follows, viz.:
It having pleased the Supreme Governor of the Universe, in the disposition of human affairs, to cause the separation of the Colonies of North America from the domination of Great Britain, and after a bloody conflict of eight years, to establish them Free, Independent, and Sovereign States, connected by alliances, founded on reciprocal advantages, with some of the greatest princes and powers of the earth.
To perpetuate, therefore, as well the remembrance of this vast event, as the mutual friendships which have been formed, under the pressure of common danger, and in many instances cemented by the blood of the parties, the officers of the American army do hereby in the most solemn manner, associate, constitute and combine themselves into one SOCIETY OF FRIENDS, to endure so long as they shall endure, or any of their eldest male posterity, and in failure thereof, the collateral branches, who may be judged worthy of becoming its supporters and Members.
The officers of the American army having generally been taken from the citizens of America, possess high veneration for the character of that illustrious Roman, LUCIUS QUINTIUS CINCINNATUS; and being resolved to follow his example, by returning to their citizenship, they think they may with propriety denominate themselves ---
There is actually quite a bit in Washington's writings on the group.
I should note there were, I have found, orthodox Trinitarian Christians who were involved with things such as affinity for Greco-Roman antiquity, the excessive use of reason/natural law in religion, and Freemasonry. My point is these things were 1) at the very least a-biblical, and 2) essential to understanding Founding era ideology. They were as essential as the so called "Judeo-Christian" tradition. So when folks say America's Founding has a "Judeo-Christian" Foundation or the Founding documents represent a "Judeo-Christian" worldview, they peddle, at best, a half truth. America's Founding mixed the Judeo-Christian tradition in an ideological synthesis with a noble pagan, Enlightenment and Whig worldview. Which, if any of those worldviews dominated and whether such an ideological synthesis is truly compatible with historic orthodox Christianity is a matter of debate. But there is no denying the historical reality of dynamic.
Take for instance, George Washington's dithering on the afterlife to ANNIS BOUDINOT STOCKTON, August 31, 1788:
But, with Cicero in speaking respecting his belief of the immortality of the Soul, I will say, if I am in a grateful delusion, it is an innocent one, and I am willing to remain under its influence. Let me only annex one hint to this part of the subject, while you may be in danger of appreciating the qualities of your friend too highly, you will run no hazard in calculating upon his sincerity or in counting implicitly on the reciprocal esteem and friendship which he entertains for yourself.
The felicitations you offer on the present prospect of our public affairs are highly acceptable to me, and I entreat you to receive a reciprocation from my part. I can never trace the concatenation of causes, which led to these events, without acknowledging the mystery and admiring the goodness of Providence. To that superintending Power alone is our retraction from the brink of ruin to be attributed.
Now, if George Washington were a Christian in the sola scriptura, Christ only, orthodox Protestant sense (as some on the Christian America side shockingly assert) why on Earth would he appeal to Cicero as an authority for the immortality of the soul, but instead cite verse and chapter of scripture (which, despite the occasional biblical allusion, he never did)?
Or take Thomas Jefferson's letter to Richard Henry Lee, May 8, 1825, on the ideological sources of the Declaration of Independence and lists them as "Aristotle, Cicero, Locke, Sidney, &c. ..." Jefferson certainly was no orthodox Trinitarian Christian; Washington may have been (I doubt it). But one thing for sure is the "Christianity" of the key Founders, Washington's for instance, was nothing like Francis Schaeffer's, who typifies to many modern evangelicals what Christianity should be about. Even if Washington were an orthodox Trinitarian Christian, his theology downplayed orthodox doctrine and integrated natural law, Aristotelean and pagan elements. Some orthodox Christians think this perfectly fine. Many traditionalist Roman Catholics embrace their Aristotelean roots as their hero Thomas Aquinas did. But not Francis Schaeffer. See him rail against this admixture of Christian and noble pagan elements that was (perhaps unbeknownst to him) key to American Founding thought and the theology of men like George Washington.
Sure there were plenty of "Francis Schaeffers" during the era who supported the American Founding. One thinks of Timothy Dwight (President of Yale) or Jedidiah Morse (one does NOT think of John Witherspoon, President of Princeton, who himself was imbibed in the philosophical rationalism that Schaeffer argues against here). George Washington communicated with them, supported their free exercise of religion and otherwise had no problem with them. However he was not that kind of Christian and it was NOT this kind of Christianity that drove the American Founding.