A few years ago, I repeated an assertion of historical fact that is the dominant view in the academy: The beloved Bird Wilson (son of James) gave the sermon in Albany that termed all of the Presidents from Washington to Jackson "infidels," and not more than unitarians. A Brown University PhD in history named James Kabala alerted me that it was a different Wilson (a "Willson") who gave that sermon. He told me he noted this in his PhD thesis.
He has published this finding in a peer reviewed scholarly article entitled "Theocrats" vs. "Infidels": Marginalized Worldviews and Legislative Prayer in 1830s New York in the "Journal of Church and State." The article sheds light on an important and much misunderstood nuance of late 18th, early 19th Century America. Theocratic politics of the Calvinist covenanting variety, on the one hand, and deistic or atheistic infidel worldviews, on the other, were "non-respectable."
I think one could say the softer unitarian infidel worldview was also non-respectable, but was gaining respectability. In New England unitarianism became completely respectable by the early 19th Century. BUT these "unitarians" like the early Presidents whom Rev. Willson thunders against were able to "get by" because they nominally belonged to Christian churches for cover and when they started proselytizing for unitarianism they presented their creed under the auspices of "Christianity." In short, they wanted to further "reform" Christianity out of its orthodoxy. The strict deists and atheists wanted to abolish Christianity.
Despite slight disagreements with the way Dr. Kabala understands the religious views of the Founders, the article was a pleasure to read.
And I want to thank him for reference in footnote 10.