George Washington did NOT embrace the term infidel. But NONE of the key Founders, including Jefferson, Franklin or even (as far as I know) Paine embraced that term. Rather, as I have discovered, the term "infidel" meant someone to one's religious left. As Mr. Tubbs points out, Washington used "infidel" as a term of appropriation to describe those who couldn't see an interventionist God taking America's side in the Revolutionary War (against Christian Tories!). Indeed Ben Franklin likewise used the term infidel to describe those to his religious left:
Atheism is unknown there; Infidelity rare and secret; so that persons may live to a great Age in that Country, without having their Piety shocked by meeting with either an Atheist or an Infidel.
However without question Franklin, Jefferson, J. Adams, and I believe Madison and Washington were not orthodox Trinitarian Christians. That is, they were to the left of the "orthodox," who viewed the religious opinions of the key Founders as "infidelity" to "real Christianity." That's why I have termed Washington et al., "soft infidels." But since the key Founders understood how the orthodox would react to their heterodoxy, they tended to keep their religious views very guarded and private. Hence the reticence of Washington et al. to share their "religious secrets."
I recently stumbled upon a book by Timothy Dwight -- President of Yale in the Founding Era who typified "fire and brimstone" orthodox Christianity -- parts of which criticize unitarianism, particularly Joseph Priestley's opinions which, perhaps unbeknownst to Dwight, captured the minds of America's key Founders. Here is how Dwight described the "soft infidelity" of Priestley and hence of America's key Founders:
The observation of Mr. Wilberforce, therefore, seems to be but too well founded, when he says; "In the course, which we lately traced from nominal orthodoxy to absolute Infidelity, Unitarianism is, indeed, a sort of half-way house, if the expression may be pardoned; a stage on the journey, where sometimes a person, indeed, finally stops; but where, not unfrequently, he only pauses for a while; and then pursues his progress."
So what is the evidence that Washington believed in this softer form of "infidelity"? Well I've looked for Washington's connection to Priestley and have found a polite letter to Priestley (relating to science & US's emerging patent law) and one that mentions him relating to thermometers. Some other evidence connects Washington to Priestley but no "smoking guns" I have found prove Priestley to have mentored Washington's religious views as there are with Jefferson, J. Adams and Franklin.
However, Washington approved of the Unitarian Richard Price's heterodox theological views with the same zeal that he approved of Trinitarian Dr. Dwight's orthodox theological views. Washington writes the following to Rev. REVEREND ZECHARIAH LEWIS, September 28, 1798, regarding Dwight:
I thank you for sending me Doctr. Dwights Sermons to whom I pray you to present the complimts. of Yr. etc.
And compare that to Washington's approval for Richard Price's sermon critical of orthodox Trinitarian doctrine. In a letter to BENJAMIN VAUGHAN, February 5, 1785:
Sir: I pray you to accept my acknowledgment of your polite letter of the 31st. of October, and thanks for the flattering expressions of it. These are also due in a very particular manner to Doctr. Price, for the honble mention he has made of the American General in his excellent observations on the importance of the American revolution addressed, "To the free and United States of America," which I have seen and read with much pleasure.
Dwight's sermon was notoriously orthodox and Price's sermon was notoriously heterodox, yet Washington treated both of them with the same cavalier indifference. And this itself illustrates a unitarian religious attitude. It was the unitarians who tried to unite as many folks -- unitarian or trinitarian, Jew, Christian or Muslim -- together under their broad, latitudinarian theology. And it was the Trinitarians who held to the narrow path and termed the non-Trinitarians "heretics" at best, "infidels" at worst.
More evidence that Washington held to this broader, non-Trinitarian theology is he approved of the "infidel" Trinitarian Universalists, who denied eternal damnation, writing to them,
in our nation, however different are the sentiments of citizens on religious doctrines, they generally concur in one thing; for their political professions and practices are almost universally friendly to the order and happiness of our civil institutions. I am also happy in finding this disposition particularly evinced by your society.
Further Washington systematically spoke in generic philosophical titles for God (i.e., "Providence") and rarely spoke of Jesus Christ by name or person as though Washington had no personal relationship with Christ. The only two instances Washington's public or private writings speak of Jesus by name or person were written in other peoples' hand. The 1783 Circular to the States which describes Jesus (by example not name) as "divine" is at least consistent with Arianism. Indeed the open Arian Richard Price fully approved of this address noting he was “animated more than he can well express by General Washington’s excellent circular letter to the united states.” The sentiments in the Circular are even perhaps consistent with Socinianism which saw Jesus as a man on a divine mission.
Speaking of Jesus only two times (especially not written in Washington's hand) in 20,000 pages of recorded writings is not much in my opinion. That's exactly the number of times Washington referred to God as "the Great Spirit" when addressing unconverted Native Americans, something Peter Lillback has no problem waving away with his intellectual hand.
More importantly, that Washington systematically avoided communion in his Trinitarian Church cast serious doubt on the notion that he was orthodox. Washington never disclosed exactly why it was that he avoided communion so we have to look for the most common sense answer. And that is he didn't believe in what the act symbolically represents: Christ's Atonement. The deistic and unitarian minded folks in the orthodox Churches were the ones who, like Washington, got up and turned their backs on the Lord's Supper. As Washington's own minister, Dr. Abercrombie, put it specifically referring to Washington's unacceptable behavior in Church:
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.
And indeed, more evidence exists that those who avoided communion in the Anglican/Episcopal Church did so because they DIDN'T believe in the Trinity. As John Marshall's daughter put it describing Marshall's own systematic avoidance of communion in that Church:
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 ultimately with Washington we are left with unequivocal evidence that he believed in an active interventionist God but little evidence that he believed in the doctrines of orthodox Christianity. Indeed, he like the other key Founders, lived in a religious closet, as though he had something to hide. As Thomas Jefferson put it:
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 tho[ugh]t 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.