Zuckert argues Locke's influence transformed both politics and the Christian religion itself during the 18th Century. "Rational Christianity" (what Gregg Frazer terms "theistic rationalism") is what Christianity turned into after first Locke and then Jefferson, Adams et al. transformed it into something more politically useful for the age of republicanism or classical liberalism. Whether what the Founders understood as "rational Christianity" is properly termed "Christianity" at all is debatable. To America's key Founders, such "Christianity" often embraced theological heresies.
Noll notes that "republicanism" often presented itself with "Christianity" as though the two went together (hence the kernel of truth to the "Christian America" claim). However, Noll notes the genesis of republican ideas were outside of traditional Christian teachings. Hence a great "importing" of a-biblical, non-traditional teachings into Christianity during the 18th Century.
I am particularly interested in the connection between Founding era liberal or republican ideas, and theological heresy. As Noll notes, there is a connection. This, for me, is the preeminent passage in Noll's paper:
In a careful analysis of the religion of James Harrington, whose Oceana of 1656 was the era's fullest statement of republican principle, Mark Goldie has spelled out the conditions under which republican and Puritan views could move beyond simple cooperation against a common foe. The key, according to Goldie, was the softening of Puritan theological orthodoxy: when Puritans remained committed to traditional Christian ideas of human depravity, the sovereignty of divine grace, and the need for a revelation from God, they also remained antagonistic to republican ideas. But, in Goldie's phrase, "wherever puritan thought leaned towards acceptance of the possibility of universal salvation and hence of universal priesthood, or to the Socinian idea that Christ was God-in-humanity, then Puritanism became as intensely secular and naturalistic as it was Biblical and Apocalyptic." Most observers in the seventeenth and eighteenth centuries would have agreed. It was only when Christian orthodoxy gave way that republicanism could flourish.
A long line of distinguished modern historians--including Caroline Robbins on the English commonwealthmen, J. G. A. Pocock on Machiavelli, Paul Rahe on the republican traditions more generally, J. C. D. Clark on eighteenth-century English society, and J. B. Schneewind on the rise of moral philosophy--has documented the persistent link during the centuries before 1750 between political republicanism and such heterodox religious views as Socinianism, Arianism, Unitarianism, and atheism. Of special note was the tie between republican views of human nature that transferred responsibility for the health of society from God to humanity and unorthodox views (whether Socinian or Arian) concerning the person of Christ. For the latter, Jesus was a good man and valuable for his example of personal morality, but he was not the son of God whose saving work opened the only door to human salvation.
An expressly religious suspicion of republican ideas continued widely in the new world. The American Samuel Johnson was outraged when Trenchard and Gordon's Independent Whig was reprinted in New York City at mid-century. To Johnson as a traditional Anglican, the Real Whig arguments were "pernicious" outbursts from "famous infidel authors." He was not alone in these opinions. Other New Yorkers accused the sponsors of the Independent Reflector, where Trenchard and Gordon were reprinted, of being atheists and noted that its publisher, James Parker, had been indicted for "blasphemous libel" against Christianity only shortly before reprinting these English Real Whig opinions.
The long history of antagonism between republicanism and traditional Christianity therefore poses a major interpretive problem for students of American history, since, in the carefully chosen words of philosopher Charles Taylor, "for all the well-documented tensions between Christianity and the republican tradition, the United States starts its career by linking the two closely together."