My comments with respect to deists were very much directed at our "founding fathers" who were, not surprisingly, probably more liberal and anti-authoritarian in their leanings than many of their peers (the rejection of orthodoxy was probably more common among the leaders of the revolution than among the balance of the delegates signing the Declaration). However, the belief that religion was primarily a matter of personal conscience was much more widely held and was probably more of a factor in the Constitutional exclusion of the government from passing any laws respecting religion or requiring any religious test (i.e., statement of belief) for holding office.
The move towards greater religious orthodoxy didn't really become a force until the end of the 18th century and early in the 19th. It was a major factor in Jefferson's Presidential campaign in 1800 (against John Adams) with the then equivalent of the religious right campaigning hard to defeat him. Jefferson won despite their opposition and despite widespread belief that he was an atheist. Jefferson also was relatively quiet about his religious beliefs, reserving his religious discussions primarily for his private correspondence. One of his frequent correspondents was Joseph Priestly and later, to the surprise of both, his former political opponent John Adams. Adams had received some details concerning the Jefferson Bible from Priestly and encouraged Jefferson to complete it.
The article you referenced in your link actually supports much of what I say although it appears to have a very specific agenda of trying to formulate arguments to dilute the intentions of the establishment clause. I do disagree with some of the author's facts, including his classification of John Adams as a Universalist Unitarian. The first Universalist church in America was not formed until 1779 by John Murray and the link between Universalists and Unitarians did not emerge until the 20th century, being formalized in 1960. Until the time of the merger, a key distinction between the two was the universalism, while it rejected the notion of damnation, attributed universal salvation to Christ and accepted his deity. Unitarians did not. When the two religions merged, it was based on a complete rejection of religious creed in favor of personal conscience and an agreed set of principles for action. Christian and athiest Unitarians probably exist in approximtely equal numbers.