As I see it, high church Anglicanism equals (or at least strongly correlates with) Tory political theology. And America rebelled against Toryism.
Peter A. Lillback addresses this issue in his tome on George Washington's religion. I may have given the misimpression Lillback is a bad scholar along David Barton grounds. I think his book is flawed on a number of different grounds. I don't think he proves Washington was an "orthodox Trinitarian Christian." And a respectable academic editor (which the book lacks) would have taken it from 1200 pages or so to 800 to make it more organized and readable. Dr. Lillback is nonetheless a legitimate scholar.
But Lillback argues that Washington was a "low church Anglican." Indeed, I would say Washington fit into the "low church latitudinarian Anglican" wing. The problem (for those who support Lillback's thesis) is that wing, because of its doctrinal latitude did indeed include Trinitarians of the Calvinist bent and otherwise, but also included more deistic and unitarian minded theists as well (they were also often called "liberal dissenters").
The "high church" wing took Anglican doctrine more literally. They were not "latitudinarian." Arguably they were more "Anglican fundamentalists" in the sense they took everything their church officially taught literally.
Indeed, one mild criticism of Gregg Frazer's new book which lays out the case for the American loyalists is that it's almost entirely (but not entirely, there was at least one Presbyterian loyalist minister) drawn from Anglican sermons preaching high church Anglican Tory doctrine of submission to the monarchy and parliament in the face of Romans 13.
Since George Washington systematically spoke about God in generic terms, never mentioning Jesus in his private correspondence, etc., the only way to make him into a Trinitarian is through Anglican doctrine (which is explicitly Trinitarian). And Lillback tries to make Washington into an "oath fundamentalist." Washington did indeed take Trinitarian oaths when becoming a vestryman and a godfather. Jefferson took those oaths when becoming a vestryman, but refused to be a godfather because of their Trinitarian nature. Jefferson was driven nuts thinking about the Trinity. Washington was not.
But the problem is those oaths are high church! They demand allegiance and obedience to the King as head of church and state. It's actually quite fascinating that so many notable American founders were Anglicans who rebelled against mother England and then became Episcopalians. And it's not just laity. There were ministers, some more orthodox than others, who also supported the rebellion. And others, more high church oriented, who remained loyalists.
When trying to explain why Washington systematically avoided communion in the church, Lillback stressed Dr. Abercrombie -- the minister who called Washington out as either a "deist" or not a "real Christian" for avoiding communion -- was a Tory loyalist. In other words, GW didn't want to be in communion with this guy. But, any Anglican who supported the rebellion technically had a problem with official Anglican doctrine.
One of the Anglican leaders who testified that Washington avoided communion, Bishop William White, actually supported the rebellion. This is what his Wiki page notes: "Though an Anglican (Episcopalian) cleric who was sworn to the king in his ordination ceremony, White, like all but one of his fellow Anglican clerics in Philadelphia, sided with the American revolutionary cause."
Interestingly, that footnote 6 says:
Only William Stringer, a recent immigrant f[ro]m Ireland in 1773, remained a Loyalist among the Anglican clerics in Philadelphia. In a Letter to Lord Dartmouth on March 6, 1778, from Philadelphia, Stringer reports that he is the only clergyman in Philadelphia who has acted consistent with his ordination oath of allegiance to the King and duty as a minister. See The Manuscripts of the Earl of Dartmouth, Volume 2, p. 460.Bold face mine.
After America's revolution succeeded, by necessity the Anglican churches had to "reform" their doctrines to scrub the language of the British monarchy technically ruling over them. From what I know, all but one became Episcopalians who left most everything in place, except that language that needed scrubbing.
Though one Anglican Church in New England, King's Chapel used the opportunity to reform itself into unitarianism. Its Wiki page says:
It became Unitarian under the ministry of James Freeman, who revised the Book of Common Prayer along Unitarian lines in 1785. Although Freeman still considered King's Chapel to be Episcopalian, the Anglican Church refused to ordain him. The church still follows its own Anglican/Unitarian hybrid liturgy today.