The following is a good article by Orv Breitkreutz & Dr. Peter Gibbon on George Washington's religion (though it does, alas, slightly misquote GW's address to the Delaware Indians).
Here is a taste:
Several of the articles and books that were included in our assigned readings in the last three weeks have included allusions to George Washington’s religious beliefs, or lack thereof. We have learned that a variety of religious groups have claimed Washington’s allegiance, especially among the evangelical groups that became prominent in the nineteenth century. I recall, when visiting Freedom’s Foundation at Valley Forge a number of years ago, being impressed by the large statue of George Washington kneeling in prayer, apparently based upon Parson Weems’s dubious story so popular in both the nineteenth and twentieth centuries. Even in the twenty-first century, television evangelists like Dr. James Kennedy and Timothy LaHaye (author of the Left Behind books) have claimed the General as a devout evangelical Christian. However, historians such as Peter Henriques call Washington a “theistic rationalist” who followed a “hybrid belief system mixing elements of natural religion, Christianity, and rationalism, with elements of rationalism being the predominant element.” Our astute historian Frank Grizzard, who has worked with the organizing and digitizing of Washington’s works for years, characterizes his religious beliefs as a mix of principles common to Stoicism, Freemasonry, and Christianity, in which Providence was conceived of as an “ ‘omnipotent,’ ‘benign,’ and ‘ beneficent’ Being that by ‘invisible workings’ in ‘infinite wisdom’ dispensed justice in the affairs of mankind. Astonishment and gratitude were owed this Being.” Many have expressed a bit of frustration because Washington seemed so reticent and reluctant to write down exactly what he believed concerning religion. In a famous letter to Dr. James Anderson (24December1795), we have evidence that he viewed his religious beliefs as “few and simple”:...
The article endorses Mary V. Thompson's (of Mount Vernon) "Latitudinarian" thesis. Thompson's "In the Hands of Good Providence: Religion in the Life of George Washington," is on my list. I've heard very good things about it.
I think the "latitudianarian" thesis is more or less correct, insofar as it does not contradict the "Christian-Deist," "theistic rationalist," "unitarian" thesis. These are, arguably, all different ways of saying the same thing. For instance, one could be a "Thomist," a "Roman Catholic," and an "orthodox Christian" without contradiction. Ditto with a "Presbyterian," a "Calvinist," and an "orthodox Christian" and so on.
There is a potential misuse of the latitudinarian thesis: In his 1200 page tome, Peter Lillback recognizes GW's latitudinarianism, but argues said movement was constrained by orthodox Trinitarian grounds.
Long story short: There was a "Latitudinarian" movement within the English Anglican Church. From the NEH article, quoting scholar D.F. Wright:
[Latitudinarians] became prominent churchmen. They included John Tillotson, Archbishop of Canterbury; Edward Stillingfleet, Bishop of Worcester; Simon Patrick, Bishop of Chichester and Ely; Gilbert Burnet, Reformation historian and Bishop of Salisbury; and Thomas Tenison, Archbishop of Canterbury. They reacted against the Calvinism of the Puritans and were broadly Arminian in outlook. They aligned themselves with progressive and liberal movements in the contemporary intellectual world....
Their comprehensiveness allowed only a narrow core of fundamentals in religion. They resisted the Laudian or High Church insistence on conformity in nonessentials such as church order and liturgy.
The capital L Latitudinarian movement occurred in late 17th Century England. They were friends with John Locke. It was still illegal to deny the Trinity in England during this time (it remained so until 1813). So, though the Latitudinarians were suspected of Arianism, Socinianism, few left smoking gun evidence of such and a case could be made that that movement occurred within orthodox Trinitarian grounds.
The problem is Washington was not part of that movement. He didn't call himself a "Latitudinarian" (just like he didn't call himself a "Deist," a "Unitarian" and rarely called himself a "Christian" either) or appeal to the authority of the figures named on that list. (And, though he commonly made biblical allusions as did practically everyone back then, he never proof quoted the Bible.)
Rather, Washington expressed a latitudinarian attitude on religious doctrine. Washington's latitudinarianism, based on the words he left, was constrained on Providential, not orthodox Trintiarian, grounds. That makes GW's latitudinarianism not meaningfully different from the Christian deism and unitarianism of the other "key Founders" (Jefferson, J. Adams, Franklin, etc.).
Indeed, the NEH article aptly defines what this theological system (whatever we term it) boils down to:
One early proponent is said to have reduced the Thirty-Nine Articles of the Anglican Church to five: “That God exists, that he should be worshiped, that man should order his faculties as the principal part of divine worship, that everyone is duty bound to repent his sins, and that rewards and punishments will follow our brief passage here” (Thompson 5).