I tend to focus on John Adams so much to explicate the political-theology of the American Founding precisely because he is properly regarded as so "mainstream" a figure. There is a tendency to note (improperly) that Thomas Jefferson and Ben Franklin were "Deists" (in the strict sense of the term, which they weren't) and cast them off as outliers. Well, whatever their political differences, John Adams believed virtually exactly as did Jefferson and Franklin on their personal religious creed. And this tells me just how mainstream this personal creed was among the notable Founding Fathers.
They were "rationalists" in the sense that they believed the Bible was partially inspired and reason was the ultimate determiner of truth, including what parts of the Bible were legitimately revealed. The natural law [or as they put it in the Declaration of Independence, "the laws of nature and nature's God"] was that substantive law -- both scientific and moral -- which man could "discover" thru the use of his unaided reason. Though they believed some connection between the natural and revealed law (the same God who wrote the natural law also PARTIALLY inspired the Bible) the key Founders elevated natural (what man discovered from reason) over revealed (what's written in the Bible).
At least that is what John Adams does in his letter to Jefferson Sept. 12, 1813. Adams elevates reason so far over revelation that he notes even if he were on Mt. Sinai with Moses and God told him of the Trinity he still couldn't believe it because reason proves 1+1+1=3, not 1. Even as a secular minded fellow, I can see this as an arrogant elevation of reason over all else. As Adams noted:
. . . the human Understanding is a revelation from its Maker which can never be disputed or doubted. There can be no Scepticism, Phyrrhonism or Incredulity or Infidelity here. No Prophecies, no Miracles are necessary to prove this celestial communication. This revelation has made it certain that two and one make three; and that one is not three; nor can three be one. We can never be so certain of any Prophecy, or the fulfillment of any Prophecy; or of any miracle, or the design of any miracle as We are, from the revelation of nature i.e. natures God that two and two are equal to four. Miracles or Prophecies might frighten us out of our Witts [sic]; might scare us to death; might induce Us to lie; to say that We believe that 2 and 2 make 5. But we should not believe it. We should know the contrary
Had you and I been forty days with Moses on Mount Sinai and admitted to behold, the divine Shekinah, and there told that one was three and three, one: We might not have had courage to deny it. But We could not have believed it.
The whole thing is worth reading. Adams also denies eternal damnation and notes the dynamic that still persists to this day of orthodox Trinitarians not considering his theology to be "real Christianity," to which Adams responds:
Howl, Snarl, bite, Ye Calvinistick! Ye Athanasian Divines, if you will. Ye will say, I am no Christian: I say Ye are no Christians: and there the Account is balanced [sic]. Yet I believe all the honest men among you, are Christians in my Sense of the Word . . . .