That is, a scholar imbibed in the rich intellectual traditions of Judaism might focus on the Hebraic sources, a Baptist on their contributions, the Calvinists on theirs, and Roman Catholics can find "accidental Thomism" from a Protestant people who were by in large, anti-Roman Catholic.
And there certainly is a strong kernel of truth to each critique. The individual ideas that became en vogue by the Enlightenment religionists tended not to be new. For instance, freed from the constraint of the Magisterium and with each believer a priest entitled to interpret scripture for himself, many notable Protestants became Arians. After all, the Bible never specifically uses the term "the Trinity."
Arianism was the dominant theology of the 18th Century enlightened unitarians. But Arianism is old. Quite old indeed. Even the more radical forms of unitarianism or "Christian-Deism" that for instance, Thomas Jefferson might endorse were found in the early Church. Jefferson didn't cite Marcion much, but their personal theologies were quite similar.
Speaking of Jefferson below is a quotation of his that typified the "Enlightenment" perspective on Christianity:
Were I to be a founder of a new sect, I would call them Apriarians, and after the example of the bee, advise them to extract honey of every sect.Lest you think I cite Jefferson as some kind of "outlier," here's a more mainstream orthodox Trinitarian Christian, albeit a universalist, making a similar point:
-- Thomas Jefferson to Thomas B. Parker, May 15, 1819.
It would seem as if one of the designs of Providence in permitting the existence of so many Sects of Christians was that each Sect might be a depository of some great truth of the Gospel, and that it might by that means be better preserved. Thus to the Catholics and Moravians he has committed the Godhead of the Saviour, hence they worship and pray to him; to the Episcopal, Presbyterian, and Baptist Church the decrees of God and partial redemption, or the salvation of the first fruits, which they ignorantly suppose to include all who shall be saved. To the Lutherans and Methodists he has committed the doctrine of universal redemption, to the Quakers the Godhead and influences of the Holy Spirit, to the Unitarians, the humanity of our Saviour... Let the different Sects of Christians not only bear with each other, but love each other for this kind display of God's goodness whereby all the truths of their Religion are so protected that none of them can ever become feeble or be lost.
-- Benjamin Rush, "Commonplace Book," August 14, 1811. Corner, Autobiography of Rush, 339-340.In short, the "enlightened" Protestant Christian used his own "judgment"-- his "reason" or otherwise -- to decide for himself how to interpret the faith, in what doctrines to believe, which parts of the Bible are inspired, which books, in fact, belong in the canon, and what political principles ought be derived from a "proper" understanding of theology.
So how did this impact the relationship among Enlightenment, Christianity, and the American Founding? Everything we "value" about the political-theology of the American Founding (and some things that we don't) probably can be found in bits and pieces during earlier more "traditional" periods. But it didn't all come together until these enlighteners used their reason "to extract honey of every sect" as Jefferson put it, at the exact moment they did. During that period historians term "the Enlightenment."
For instance, the "Calvinist resisters" (though not Calvin himself) might have something to offer like "rebellion against tyrants is obedience to God." Though, they were woefully deficient on religious liberty. Likewise, the Thomists incorporated a theistic grounding for Aristotelian rationalism but likewise were deficient on religious liberty and other matters.
Roger Williams and the Quakers were considered novel and eccentric when they innovated the "Christian" case for religious liberty. (That's where one had to go for this teaching, not the Calvinist resisters or those Protestants who borrowed from the scholastics.) The enlighteners of the 18th Century, using their reason, took from them this principle and combined it with what they saw the best from the other traditions to deliver the liberalism that founded America.