Another money quote:
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.
Some of my co-bloggers note, perhaps correctly, that rational Christianity didn't "import" anything new. The "rational Christians" may well have rediscovered or reinvigorated old Christian "heresies" like Arianism, Socinianism, Universalism, etc.