Over the years, I've witnessed and been involved in very meticulous debates over the America's Founding Fathers and their religious beliefs. One reason why the different sides can come to such differing conclusions on matters like "what was George Washington's religious faith?" is the historical record contains some ambiguities.
That's where presumptions and smoking guns come into play. No matter what one's presumption, when you have smoking gun quotations (like, for instance, when Jefferson explicitly rejected EVERY single tenet of orthodox Christianity as he did in his October 31, 1819 letter to William Short) then usually one concedes the point. If there aren't smoking gun quotations but rather "pieces" of the puzzle to put together, each side tends to resolve the ambiguities in favor of a particular presumption.
At bottom of this "Christian Nation" idea, I see a presumption -- one I find to be an utter historical myth with no foundation in the record or in how orthodox Christians themselves are supposed to interpret the Bible -- that just about all of the "Founding Fathers" were devout, regenerate, orthodox Trinitarian Christians (some even go so far and state "evangelical" or "born-again") and only if it can be shown beyond a reasonable doubt with smoking guns (like the above mentioned Jefferson's letter to William Short) should that presumption be overcome.
What the record actually shows is that virtually all of the Founding Fathers had some type of formal or nominal association with a "Christian Church" (like the Anglican, Congregational, etc.) all of which in the 18th Century professed orthodoxy in their official creeds. Likewise, almost all in the population considered themselves "Protestant Christian" in some formal sense, even if many or most were un-churched.
In that broad way, nominal-Christian sense, I would concede all of the "key" Founding Fathers -- Washington, J. Adams, Jefferson, Madison, Franklin -- to be "Christians." Indeed, I consider nominal or broad-way Protestant Christianity (that which encompasses all sorts of theologically liberal heresies) to be a key component of America's public Founding (and a key component of "theistic rationalism").
But that's not how traditional orthodox Christians understand "Christianity." As as I read the Bible, and understand the traditional orthodox Christian view of the creed, true Christianity is a narrow path. Since the Bible talks about the true path as so narrow, most orthodox Christians concede that "real Christians" are only a minority in any given population at any given time -- even in nations whose demographics are predominantly or exclusively "Christian."
Even in colonial era America, when the colonies were under theocratic rule, when they were far more "traditionally religious" than during America's Founding era from 1776-1800, orthodox Christians may want to pause before claiming a "majority" of its citizens. One of the earliest proponents of religious liberty and separation of Church & State, Roger Williams, an uber-orthodox Christian, was convinced the majority of his fellow colonial era Americans were NOT real Christians in the regenerate sense. Indeed, he thought in part because of the inevitable presence of so many non-regenerate folks in any country it was utterly blasphemous for any "nation" to call itself "Christian" even though some real Christians were in it.
One notable study of the religiosity of late 18th Century America found it to have a distinctively un-churched population with only as 17 percent as regular church goers. James H. Hutson has noted this study may be a lowball, that as many as 70 percent may have been regular churchgoers. But even if we concede the 70 percent figure, orthodox Christians still can't presume that all or even most of them were "real," regenerate Christians, as opposed to nominal Christians. Indeed, their faith tells them they can't presume this.
What is defined as "theistic rationalism"/"unitarianism"/"Christian-Deism" is just a highly intellectualized version of the generic, nominal Christianity that arguably has always had a strong presence in the pews of Christian Churches.
John Derbyshire, referring to his own nominal Anglicanism, once said something along the lines of the lazy Christian mind is reflexively Deist. Studies today show that the dominant belief among young people in Christian Churches is not orthodox Christianity but "Moralistic Therapeutic Deism" (the linked article inaptly refers to this creed as "new"). Likewise Jefferson once said, "I remember to have heard Dr. Priestley say, that if all England would candidly examine themselves, and confess, they would find that Unitarianism was really the religion of all...." The following from Madison on George Washington's faith likewise illustrates the "unthinking" unitarianism of a man who didn't identify as such. Madison said he did "not suppose that Washington had ever attended to the arguments for Christianity, and for the different systems of religion, or in fact that he had formed definite opinions on the subject."
Unthinking unitarianism is simple belief in God and attachment to the Christian religion without care or concern about doctrines one way or the other. Here Alexander Hamilton, in describing what he looked for in a wife, explicates this radical doctrinal indifference. "As to religion, a moderate streak will satisfy me. She must believe in god and hate a saint."
Nominal Christians as they were living in an era when when orthodox Christian Churches and figures possessed much social power, America's Founders oft-had to, as Gary North put it, (describing Blackstone) "tip the brim of their epistemological caps to God and the Bible, but they did not take off their caps in the presence of God."
Likewise when these nominal Christians made nominal references to Christianity and scripture, many apologists for the Christian Nation thesis (see here, here, here and here) use this as an opportunity to "read in" to the record orthodox Trinitarianism, the Bible is infallible, regeneration, evangelicalism, being "born-again" and all sorts of other things they associate with "real Christianity." For instance, if Jefferson hadn't told us what he really believed in in his private letters, could you imagine what these apologists would do (or have done!) with the following quotation of his from his Second Inaugural Address:
I shall need, too, the favor of that Being in whose hands we are, who led our forefathers, as Israel of old, from their native land, and planted them in a country flowing with all the necessaries and comforts of life; who has covered our infancy with his providence, and our riper years with his wisdom and power; and to whose goodness I ask you to join with me in supplications, that he will so enlighten the minds of your servants, guide their councils, and prosper their measures, that whatsoever they do, shall result in your good, and shall secure to you the peace, friendship, and approbation of all nations.
This was coming from the mouth of a man who was a former Vestryman in the Anglican Church and simultaneously rejected "[t]he immaculate conception of Jesus, his deification, the creation of the world by him, his miraculous powers, his resurrection and visible ascension, his corporeal presence in the Eucharist, the Trinity; original sin, atonement, regeneration, election, orders of Hierarchy, &c."
The Christian Nation apologists attempt to argue Jefferson was a religious outlier, but this isn't so. As noted, John Adams, generally understood to have political and religious views mainstream for the Founding Fathers, had religious views nearly identical to Jefferson's. And there is little in the historical record that shows Washington, G. Morris, Wilson, Madison or Hamilton (before the end of his life, after his son died in a duel) to have personal religious views that differed at all from Jefferson's, Franklin's and J. Adams'.
Hopefully this explains why it is that I will not give Washington, Madison, Hamilton, Wilson the "benefit of the doubt" and presume ANY kind of orthodox Trinitarianism, regeneration, belief that the Bible is infallible because I think those arguing for such have the burden of so demonstrating.