The following is taken from the notes of Thomas Jefferson on February 1, 1800, and the subject is George Washington's lack of belief in the Christian religion.
Dr. Rush tells me that he had it from Asa Green that when the clergy addressed Genl. Washington on his departure from the govmt, it was observed in their consultation that he had never on any occasion said a word to the public which showed a belief in the Xn religion and they thot they should so pen their address as to force him at length to declare publicly whether he was a Christian or not. They did so. However he observed the old fox was too cunning for them. He answered every article of their address particularly except that, which he passed over without notice. Rush observes he never did say a word on the subject in any of his public papers except in his valedictory letter to the Governors of the states when he resigned his commission in the army, wherein he speaks of the benign influence of the Christian religion.
I know that Gouverneur Morris, who pretended to be in his secrets & believed himself to be so, has often told me that Genl. Washington believed no more of that system than he himself did.
That little passage is very telling and hopefully sheds light on the Christian v. Deist controversy about our Founding. As I've discovered in researching this issue over the past few years, both sides posit myth. The secular side argues, "our founders were almost all Deists" and the other side, "our founders were almost all orthodox Christians." The truth is far more nuanced and lies somewhere in between.
We know from their writings that founders like Jefferson, Adams, and Franklin explicitly rejected the tenets of orthodox Christianity. However, their most anti-clerical and radical rejection of orthodoxy came from their private correspondence. Thomas Paine was very public about his unorthodoxy and was personally ruined for it. Jefferson was almost ruined by the tamer stuff (than what we see in his personal letters) he wrote about religion in Notes on the State of Virginia. And Adams's Federalist clergy supporters in the 1800 election (Jefferson's enemies) apparently were completely unaware of Adams's unorthodox beliefs and would have flipped out if they were privy to the anti-clerical content in the letters he wrote to Jefferson (later in their lives).
Back then one could not get in social or legal trouble for publicly affirming the tenets of orthodox Christianity, but one likely would get in trouble for publicly denying such tenets. We even see from the above passage that, if one was silent as to one's religious beliefs, there was strong social pressure to affirm publicly one's orthodoxy. And that's something neither George Washington nor James Madison did.
In my humble opinion (and apparently in Jefferson's and Morris's), Washington's (and Madison's) silence on their personal religious beliefs points in the direction of their belief in the deistic-unitarian natural religion in which Jefferson, Adams, and Franklin believed.
Understanding this helps to demonstrate the main flaw in the late M.E. Bradford's categorization method where he notes that only three of the signers of the Constitution were "Deists," the rest professed orthodox Christianity. This is so misleading that it becomes factually false. Bradford simply looked at those founders who were open "Deists" and had no connection with any Christian Church and put them in the Deist box. All of the other Founders were in some way connected to a Christian Church. Bradford's "Deists" were Hugh Williamson of North Carolina, James Wilson and Benjamin Franklin of Pennsylvania. So men like Washington, Madison, and Morris, because they were in some way affiliated with "Christian" Churches, were "orthodox Christians." Were Jefferson a signer of the Constitution, he too would have been put in Bradford's "orthodox Christian" box.
There is simply no credible historical evidence that "Christians" like Washington, Madison, Morris, and many other signers of the Constitution had personal religious beliefs that differed in any meaningful way from Jefferson's and Franklin's. In short, Bradford's analysis fails to deal with the fact that many Founders whom he categorizes as "orthodox Christians," were exactly like Jefferson: They only nominally belonged to their Churches, privately rejected the tenets of orthodox Christianity, and otherwise possessed unorthodox beliefs. They were, "in the closet," so to speak, about their unorthodoxy.
Not intending to make an analogy to homosexuality, but whenever there is social and/or legal pressure against X, those who are involved with X tend to "be in the closet." Washington and Madison, and to a lesser extent, Adams, were closet heretics. Jefferson was less so but not as "out" as some people think he was. Thomas Paine was totally "out" and had his public reputation ruined for his candor.
And these founders didn't approve of the way in which the forces of "religious correctness" could exert such power. They looked forward to the day where not only could people wear their religious unorthodoxy on their sleeve but when their unorthodox heretical beliefs would transform the Christian religion itself. As Jefferson wrote in 1822, "I trust that there is not a young man now living in the United States who will not die a Unitarian."
While Jefferson was wrong in the speed in which unorthodoxy would replace orthodoxy, there certainly was a kernel of reality to his prediction. Think about how many orthodox religions have now incorporated unorthodox beliefs. Think about how many Christian Churches now have openly gay ministers and would perform same-sex weddings. Even in Jefferson's time, think about how the Puritan Congregational Churches of Massachusetts became Unitarian Congregations.
We have those Founders to thank for such changes.