John Jay, not a "key Founder" but a 2nd tier Founder, is generally conceded as an "orthodox Christian." He certainly has a number of quotations that support the "Christian Nation" thesis. From most of what I've read, I'd say the categorization is accurate. Though, I've reproduced before, and will reproduce again quotations from Jay affirming the Bible, but doubting the Trinity.
In a letter to Samuel Miller, Feb. 18, 1822, Jay wrote:
"In forming and settling my belief relative to the doctrines of Christianity, I adopted no articles from creeds, but such only as, on careful examination, I found to be confirmed by the Bible."
To the Sola Scripturaist that sounds good. After all, church doctrine can be tainted with man's doctrines. But, Sola Scriptura without creeds led Jay to doubt the Trinity. From that very letter:
"It appeared to me that the Trinity was a Fact fully revealed and substantiated, but that the quo modo was incomprehensible by human Ingenuity. According to sundry Creeds, the divine Being whom we denominate the second Person in the Trinity had before all worlds been so generated or begotten by the first Person in the Trinity, as to be his coeval, coequal and coeternal Son. For proof of this I searched the Scriptures diligently -- but without Success. I therefore consider the Position of being at least of questionable Orthodoxy."
I want to focus more on Jay's disregard for creeds and how that relates to the political theology of the American Founding.
The late ME Bradford did a study where he "found" 52 out of 55 Founding Fathers in some way connected to churches that adhered to an orthodox creed. Christian Nationalists have run with that figure with a talking point that argues "52 out of 55 delegates to the Constitutional Convention were orthodox Christians."
Some Christian Nationalist (not sure if it was Bradford himself) mistakenly claimed the 52/55 figure found "membership" at a time when membership required oaths to official church doctrine.
I've looked into this in detail and the figure does not relate to "membership" but "affiliation." There is NO EVIDENCE that 52/55 took membership oaths (although some/many of them did). Alexander Hamilton, for instance (not one of Bradford's "Deists") had affiliations with both the Episcopalian and Presbyterian Churches (the two churches from whom he sought communion on his deathbed) but was never a MEMBER of either or any church during his adult life.
Bradford's figure is worthless. In fact, all 55, even his 3 "Deists" -- Franklin, Wilson, and Williamson -- had affiliations with churches that professed orthodoxy in their creeds.
Therefore, a counter to the Bradford figure that shows the vast majority of FFs connected to orthodox churches is that those affiliations were for social reasons, that, whether official members or unofficial affiliates, it was not uncommon for elites to belong to orthodox churches while disbelieving in what the churches taught as formal doctrine.
The response, I've heard, is that makes them hypocrites. Perhaps. And that's a charge those making the claim have deal with, not us who argue against Christian Nationalism. Keep in mind the Anglican Church preached loyalty to the crown as a political-theological doctrine. And many American Anglicans, most notably George Washington, remained so while rebelling against England. How is that any less hypocritical than disbelieving in the Trinity, even though your church holds to it as an official doctrine and may make you take an oath to it if you want to get involved in leadership positions(which again, many FFs used as a social network)?
But back to John Jay. He too was an Anglican who rebelled against Great Britain. In fact he was (apparently) a warden of this church.
I've seen many Christian Nationalists try to use church affiliation/membership, and especially leadership positions (which did require oaths) as shortcuts to prove the "orthodoxy" of a particular Founder. The shortcut is needed in the absence of quotations supporting the orthodox Christianity of a particular Founder. For instance, George Washington offers little if anything from his own mouth to prove he believed in the Trinity, Atonement, Resurrection of Christ. So Peter Lillback uses his Anglican affiliation as a surrogate.
Likewise with John Jay we could argue, since he was an Anglican, indeed a Church warden required to take oaths to official Anglican doctrine (which were orthodox), and since John Jay offered other quotations which seemed to support orthodox Christian doctrine, we could conclude Jay believed in official orthodox Anglican doctrines.
But no, the above offered quotations refute that. It's true that late 18th Cen. Anglicanism supported the idea of the Bible as divinely inspired in an inerrant, infallible sense (something to which Jay apparently believed). It also made the Trinity central to its creed. AND relied on official creeds like the Athanasian Creed and 39 Articles of Faith to clarify just how they interpreted Word of God. And those, apparently, to Jay at that point in his life, meant little if anything to him.
In that letter to Rev. Samuel Miller, Jay was being a very bad orthodox Anglican from that perspective. If he affirmed the Trinity from Sola Scriptura but disregarded the creeds and 39 Articles of Faith, we could say Jay was being a good orthodox Christian, but not a very good Anglican (that's what evangelicals might wish because, as mostly non-Anglicans, they don't care about Anglican doctrine). But he doesn't even do that. Rather, he sounds more like a quasi-Quaker whose belief in "no creed but the Bible" led them to be wobbly on the Trinity and other orthodox doctrines.
But anyway, the Jay quotes support the notion that many late 18th Cen. American orthodox Churches functioned as social networks and members and affiliates didn't necessarily believe in what their churches held as a matter of official doctrine. The official doctrines of those churches CANNOT be used as shortcuts to determine what the Founders believed.