Last week my Dad and I saw Gordon Wood speak at the James Madison Program at Princeton University on the Founding Fathers.
Of course I paid close attention to his comments on the religion of the Founders when that question was asked. He avoided the term "Deist" -- a term he had once used -- and instead opted for "proto-unitarian." This shows he's paying attention to the evolving understanding in scholarship that shows the key Founders were not strict Deists like Thomas Paine and Ethan Allen. The term "unitarian" has to be qualified because it is associated with a particular Church of which only John Adams (and his son) were members. And even with Adams' Church, though it preached unitarianism as of 1750, it didn't officially become "Unitarian" until the 19th Century. Jefferson, Madison, and Washington were all theological unitarians who were formally members of the Anglican/Episcopal Church, which held to a Trinitarian creed. Besides theological unitarianism, these Founders also believed in theological universalism, syncretism, rationalism. So if we want a common term to describe the religious beliefs of the 5 key founders -- the first four presidents and Ben Franklin -- "proto-unitarian" might do, as well as some others, for instance "theistic rationalism."
There is no doubt that Jefferson was such a "unitarian," as he embraced the label and called himself one. I haven't found quotations from Washington or Madison where they call themselves "unitarian," however they never personally confessed Trinitarian Christianity, and otherwise systematically used generic philosophical terms for God (i.e., nothing identifiably Trinitarian).
[Note: Some will take issue at this last sentence because Washington, as a condition of becoming a vestrymen and godfather, took Trinitarian oaths. Jefferson likewise took those oaths when becoming a vestryman, but refused to be a godfather; the oaths could be viewed as perfunctory. The pietists argue if one takes an oath to which something one doesn't believe, one is a hypocrite. That's their judgment. Washington's refusal to take communion, which I discuss below, violated those very oaths.]
The context of the time was they were leaving an era where folks could suffer criminal penalties, sometimes death, for denying the Trinity. In their era, some states still imposed legal penalties for such, but otherwise denying the Trinity could greatly damage one's public reputation, which, as "men of honor," they strongly guarded. Ultimately, they wanted men to be able to express freely without fear of legal or social punishment what the orthodox termed “infidelity” or “heresy" (because they believed the unitarian "heresies" were right, the Trinity erroneous). And by the 19th Century, at least in the North East, "Unitarianism" became a socially acceptable form of liberal Protestant Christianity.
In the 18th Century, Deism and theological unitarianism were popular, not among the masses, but among elite educated Whigs (similar to the way in which 1960s' counterculture thought was unpopular among the masses, but popular in various college and youth circles. Think of Joseph Priestly as sort of the Founders' Abbie Hoffman).
For these reasons, I believe when prominent 18th Century figures systematically used generic philosophical terms for God and avoided using explicitly Trinitarian terms (as social forces dictated they should) this strongly suggests disbelief in Trinitarianism.
Other clues show Washington and Madison to be theological unitarians like Jefferson, Adams, and Franklin. A notable 19th Century gentleman George Ticknor dined with James Madison and reported the following:
[Madison] talked of religious sects and parties and was curious to know how the cause of liberal Christianity stood with us, and if the Athanasian creed was well received by our Episcopalians. He pretty distinctly intimated to me his own regard for the Unitarian doctrines.
Washington systematically refused to take communion in the Anglican/Episcopal Church. This has lead modern scholars to term him a "Deist." Indeed, Washington's own minister, Dr. James Abercrombie, reportedly termed Washington a "Deist" because he refused to take communion. Then Abercrombie slightly backtracked and instead noted:
“I cannot consider any man as a real Christian who uniformly disregards an ordinance so solemnly enjoined by the divine Author of our holy religion, and considered as a channel of divine grace.”
Peter Lillback, in his 1200 page book which attempts to prove Washington was orthodox Christian, argues since Washington could not have been a "Deist" (based on evidence showing Washington believed in an intervening God, prayer, and otherwise contradicted strict Deist thought) there must be some other explanation. Lillback then fabricates some political explanation that still manages to categorize Washington as an "orthodox Trinitarian Christian." In other words, Lillback knocks down a strict Deist strawman, avoids the most common sense reason for why Washington didn't commune, and then constructs, on mere speculation, a complicated political explanation just so he can place Washington in the "orthodox Christian" box.
The most common sense explanation for why Washington didn't commune was that he disbelieved in what it represented: Christ's Atonement. And logic also dictates if one doesn't believe in the Atonement, one also doesn't believe in the Trinity and Incarnation. And one need not be a "strict Deist" to disbelieve in the Trinity, Incarnation, and Atonement. Indeed, the other key Founders -- Jefferson, Adams, Franklin, and Madison -- following Joseph Priestly believed in this system of "proto-unitarianism" that denied the Trinity, Incarnation, and Atonement, yet still believed in an active personal God, prayer, the legitimacy of some revelation, and often presented itself under the label of "Christianity," not "Deism."
Finally, just because I stress certain "key" Founders as believing in this system doesn't mean other lesser Founders did not. You can add one more name to the "proto-unitarians": John Marshall, Chief Justice of the United States. And indeed, Marshall likewise was an Anglican/Episcopalian who systematically avoided communion. And here is his daughter's testimony for why he did this:
The reason why he never communed was, that he was a Unitarian in opinion, though he never joined their society. He told her he believed in the truth of the Christian Revelation, but not in the divinity of Christ; therefore he could not commune in the Episcopal Church.
So it was not just the "strict Deists" in the Trinitarian Churches who refused to commune, but also the "unitarians" some of who, like Marshall could be quite "biblical," believing in the "Christian Revelation," others like Jefferson, Franklin, and Adams, rationalists who elevated reason over revelation. And because this "unitarianism" often presented itself under the auspices of "Christianity," key contemporaneous testimony that Washington and other Founders were "Christians" is not inconsistent with the notion that they were such "proto-unitarians." Indeed, John Marshall himself was one such testifier of Washington's Christianity as was Jared Sparks. And both were "unitarians" who disbelieved in the Trinity, Incarnation, and Atonement, but still understood themselves to be "Christians." In all likelihood, so was George Washington.