Scholarly consensus holds that John Locke was the most important philosophical influence on the American Founding. Locke wasn't a deist (or as some Straussians argue a secret atheist). He called himself a Christian, defended the Christian religion as "reasonable," thought Jesus was the Messiah and may have believed much of the Bible was true. He was also almost certainly a secret theological unitarian (his Trinitarian critics smelled him out) and otherwise disbelieved in various orthodox doctrines and posited novel concepts not at all in accord with traditional Christianity. For instance his notion of Tabla Rasa denies man has a fallen, sin nature. Indeed, this led deists and "rational Christians" who embraced his teachings like Thomas Jefferson to posit the notion of the perfectibility of man.
Locke argued contra Thomas Hobbes. But what's striking about Locke's case is he didn't try to refute Hobbes by using the Bible or the classical or traditional understanding of politics. Rather, he seemed to argue against Hobbes on Hobbes' own terms: "The state of nature," an explicitly Hobbesean concept. Jean-Jacques Rousseau, who later hit the scene, did the same thing. He argued against BOTH Hobbes AND Locke, but on the grounds of the "state of nature." And as Leo Strauss correctly pointed out, the state of nature itself (be it Locke's, Hobbes' OR Rousseau's understanding of the concept) is "wholly alien to the Bible."
Though not a deist himself, Locke's teachings, in particular his idea that all truth including revelation must meet the test of reason, spawned a generation of Deists and "rational Christians" who used his method to deny the validity of parts of or the entire Bible. Voltaire, for instance, embraced Locke. One of the earliest and most noble "deist disciples" of Locke's was Lord Shaftesbury, who was literally Locke's student. (Locke actually taught/mentored him.)
In this comment discussion at American Creation, Dr. Gregg Frazer explains how Locke taught all truth must meet the test of reason and how this influenced Jefferson's and John Adams' biblical criticisms [Frazer begins his comment by responding to a nuisance who endorses the Christian Nationalist idea, one who is a terrible witness for that theory]:
When you quote someone (in this case, Locke), it is intellectually dishonest to put together two sentences which are 40 PAGES APART in the original without an ellipsis!!! This is what OFT did in the Locke quote partially addressed to me. By doing so, he wrenched Locke's words completely out of context and completely changed their meaning.
I do not have time to explain here Locke's WHOLE argument IN CONTEXT to those who are unlikely to be open to what he really said. I simply encourage interested and open readers to investigate the broader context of the quotes taken out of context from Locke's "Essay Concerning Human Understanding," Vol. II, chapters XVI-IX.
Locke summarizes his own argument thusly in italics for emphasis: "REASON MUST BE OUR LAST JUDGE AND GUIDE IN EVERYTHING." He then addresses revelation. Speaking of reason, he says: "consult it we must, and by it examine whether it be a revelation from God or no; and if reason finds it to be revealed from God, reason then declares for it as much as for any other truth, and makes it one of her dictates."
For Locke, the ultimate standard is always reason -- even for revelation.
And for ... the theistic rationalists, the same was true. They believed that there was some revelation legitimately from God (part of what separated them from the deists) -- but that was to be determined by reason.
To a ... participant in the discussion: you say "if you can find a single Founder or Founding influence who says publicly that the Bible is wrong about x because reason says so, please provide it." This is a very clever tactic on your part -- knowing that public men living in a nominally Christian environment and dependent upon public approval for their positions of power could not "publicly" say that the Bible is wrong. No politician will even do that TODAY, much less in the 18th century.
If you'll admit private correspondence (where one can see what people REALLY believed -- not what they said for public approval), you'll discover John Adams saying of the Fall of man in Genesis that it "is either an allegory, or founded on uncertain tradition, that it is an hypothesis to account for the origin of evil, adopted by Moses, which by no means accounts for the facts."
Adams likewise questioned the reliability of the Ten Commandments -- saying that "authentic copies" of the original were lost. Speaking of the coming millennial kingdom of Christ, which he identified as being founded on revelation, he said to Jefferson: "You and I hope for splendid improvements in human society .... Our faith may be supposed by more rational arguments than any of the former ...."
Adams further said: "Philosophy, which is the result of reason, is the first, the original revelation of the Creator to his creature" and that "no subsequent revelation, supported by prophecies or miracles, can supersede it." [i.e. the Bible]
Also remember that Adams said that he would not believe revelation delivered DIRECTLY to him BY GOD on Mt. Sinai if it contradicted what his reason told him about the Trinity.
Jefferson said of the Old Testament: "the whole history of these books is so defective and doubtful, that it seems vain to attempt minute inquiry into it." His favorite word for the New Testament aside from the words of Jesus was "dunghill." Even with the words of Jesus, he used his reason to separate what "genuine, and his own" from what was "attributed" to him.
If taking a pair of scissors to the Gospels and cutting out whatever one considers irrational is not saying that "the Bible is wrong about x because reason says so," then it would seem to be impossible to provide such proof.
Just in case, I'll add that Jefferson said of the rest of the New Testament that it was full of "superstitions, fanaticisms, and fabrications" along with "so much ignorance, so much absurdity, so much untruth" and "trivialities and imbecilities."
Like Locke, Jefferson said: "Whether the particular revelation which you suppose to have been made to yourself were real or imaginary, your reason alone is the competent judge. For dispute as long as we will on religious tenets, our reason at last must ultimately decide, as it is the only oracle which God has given us to determine between what really comes from him and the phantasms of a disordered or deluded imagination."
And he told his beloved nephew to "keep your reason firmly on the watch in reading" and to judge the "pretensions" of biblical writers "by your own reason."
And on and on and ....
Their standard tactic was to deny the legitimacy of the parts of the Bible (most of it) that they considered to be irrational -- that is, to deny that it was legitimate revelation from God.