Half-Way House Infidels:

That might be the title to my eventual book on the American Founding. Another title I have in mind is "Noble Pagans: America's Founding Heretics." The term "infidel" as was used during the Founding era by the "orthodox" referred to strict Deists or atheists. Theological unitarianism, in which America's key Founders disproportionately believed, was viewed as a "half-way house" towards "infidelity." That term comes from Timothy Dwight quoting Wilberforce (see below).

Theological unitarianism was believed in by very bright influential thinkers in the early and mid 18th Century, but was largely closeted then. Unitarianism began to come out of the closet in the late 18th Century. By the early 19th Century Harvard University officially became Unitarian and open Unitarians held respectable positions in American society. But the "orthodox" didn't take that lying down.

Jedidiah Morse was one of the first notable "orthodox" figures to take on unitarianism. Indeed, the closeted nature of unitarianism in the mid 18th Century is evidenced by the dialogue between Morse and John Adams. Morse, apparently, wasn't aware of the existence of American unitarians in the mid 18th Century and tried to "low ball" the length of time in which unitarians had existed in America. As John Adams acerbically wrote to Morse:

“DEAR DOCTOR,
“I thank you thank you for your favour of the 10th, and the pamphlet enclosed, entitled, ‘American Unitarianism.’ I have turned over its leaves, and found nothing that was not familiarly known to me. In the preface, Unitarianism is represented as only thirty years old in New-England. I can testify as a witness to its old age. Sixty-five years ago, my own minister, the Rev. Lemuel Bryant; Dr. Jonathan Mayhew, of the West Church in Boston; the Rev. Mr. Shute, of Hingham; the Rev. John Brown, of Cohasset; and perhaps equal to all, if not above all, the Rev. Mr. Gay, of Hingham, were Unitarians. Among the laity how many could I name, lawyers, physicians, tradesmen, farmers!...More than fifty years ago, I read Dr. Clarke, Emlyn, and Dr. Waterland: do you expect, my dear doctor, to teach me any thing new in favour of Athanasianism? — There is, my dear Doctor, at present existing in the world a Church Philosophick. as subtle, as learned, as hypocritical, as the Holy Roman Catholick, Apostolick, and Ecumenical Church. The Philosophical Church was originally English. Voltaire learned it from Lord Herbert, Hobbes, Morgan, Collins, Shaftsbury, Bolingbroke, &c. &c. &c. You may depend upon it, your exertions will promote the Church Philosophick, more than the Church Athanasian or Presbyterian. This and the coming age will not be ruled by inquisitions or Jesuits. The restoration of Napoleon has been caused by the resuscitation of inquisitors and Jesuits.
I am and wish to be
Your friend,
JOHN ADAMS”
Quincy, May 15th, 1815.

But it was Timothy Dwight, President of Yale during the Founding and post-Founding era (1795-1817), who seemed the most prolific, notable critic of newly "outed" unitarianism. You can read Dwight's criticisms of unitarianism here. Dwight spends a great deal of time attacking the work of Joseph Priestley and Richard Price. This is notable because, in a sense, Dwight attacks "thought" that was a secret "motivator" to America's "key" Founding Fathers. Men like Washington, J. Adams, Jefferson, Madison, and Franklin idolized unitarians like Locke, Newton, Clarke, Price and Priestley. Dwight writes a great deal about them which I am slowly trying to digest. However, the following quotation of his stands out as exemplifying how the orthodox thought of unitarianism:

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."