For instance, "rational" Christianity often ended up theologically unitarian and universalistic. A rational, benevolent God was unitarian not trinitarian and wouldn't consign anyone to Hell for eternity. These key FFs would say theirs was the "Christian God," properly understood; but whether such was the same God the orthodox worshipped is seriously debated.
I don't want to paint with too broad a brush. Many orthodox Trinitarian Christians of the founding era and of today are not Calvinists and are troubled by the idea of eternal damnation. Indeed Benjamin Rush's creed -- which he described as a mixture of orthodoxy and heterodoxy -- that denied eternal damnation but embraced orthodox Trinitarian doctrine might have been more mainstream than we realize and certainly seems mainstream among today's self professed Christians.
To counter this broad, tolerant reading of Christianity, the orthodox (especially Calvinists) might note Jesus said such DIVISIVE things as "I come not to bring peace, but to bring a sword"; but such statements in the Bible were anathema to the "Christianity" as endorsed by every single above mentioned key Founder. They disbelieved in the Biblical God's intolerant, jealous and vengeful nature. The only thing that likely aroused their God's wrath was violating the unalienable human rights of His children. And, as the key FF's understood God, ALL human beings were His children; many orthodox (especially Calvinists) believe if you aren't saved/regenerate, you are a "child of the devil."
The following passages quote every single above mentioned key Founder to prove the thesis. First James Wilson on Locke rejecting the intolerant, jealous, wrathful attributes of the biblical God.
The high reputation which [Locke] deservedly acquired for his enlightened attachment to the mild and tolerating doctrines of Christianity secured to him the esteem and confidence of those who were its friends. [Bold mine.]
Note Wilson qualifies Christianity with "enlightened," "mild" and "tolerating." If one argues the Bible says what it says whether we like it or not (i.e., the position of the orthodox who argue the Bible is infallible and inerrant) one wouldn't use those terms to qualify it. Consigning most human beings to Hell certainly isn't "mild" or "tolerating." Indeed the very First Commandment is neither mild nor tolerating. Quotations like this from Wilson lead me to conclude he did not believe the Bible infallible, the Trinity or eternal damnation.
Next, Alexander Hamilton defending "Christianity" against the harsh attacks of the extreme deism and atheism of the late stages of the French Revolution. Note: Hamilton probably became an orthodox Trinitarian Christian shortly before his death, after his son died in a duel. However, his defense of Christianity in the years prior was not an orthodox defense of Christianity, but rather seems a heterodox Enlightenment defense. In short, it was a "unitarian" or "theistic rationalist" defense. From Hamilton's 1794 document on the French Revolution:
It is not among the least perplexing phenomena of the present times, that a people like that of the United States—exemplary for humanity and moderation surpassed by no other in the love of order and a knowledge of the true principles of liberty, distinguished for purity of morals and a just reverence for Religion should so long persevere in partiality for a state of things the most cruel sanguinary and violent that ever stained the annals of mankind, a state of things which annihilates the foundations of social order and true liberty, confounds all moral distinctions and substitutes to the mild & beneficent religion of the Gospel a gloomy, persecuting and desolating atheism. [Bold mine.]
Again notice the qualifiers: The "religion of the Gospel" is qualified by the terms "mild" and "beneficent." Also note atheism was bad because it was "gloomy" and "persecuting." Hence Hamilton defended a religious creed judged by its benevolent and rational effects, not harsh "truth or be damned," "like it or not" standards.
Next Thomas Jefferson, from his First Inaugural Address:
Let us, then, with courage and confidence pursue our own Federal and Republican principles, our attachment to union and representative government. Kindly separated by nature and a wide ocean from the exterminating havoc of one quarter of the globe; too high-minded to endure the degradations of the others; possessing a chosen country, with room enough for our descendants to the thousandth and thousandth generation; entertaining a due sense of our equal right to the use of our own faculties, to the acquisitions of our own industry, to honor and confidence from our fellow-citizens, resulting not from birth, but from our actions and their sense of them; enlightened by a benign religion, professed, indeed, and practiced in various forms, yet all of them inculcating honesty, truth, temperance, gratitude, and the love of man; acknowledging and adoring an overruling Providence, which by all its dispensations proves that it delights in the happiness of man here and his greater happiness hereafter — with all these blessings, what more is necessary to make us a happy and a prosperous people? [Bold mine.]
Notice the qualifiers "enlightened" and "benign." As I have also documented, in his private letters, Jefferson made clear that such an enlightened version of Christianity was, in the ideal, unitarian (in fact rejected every single tenet of orthodoxy) and anti-Calvinistic. And especially notice the compatibility between the words of the supposed outlier Jefferson (which he was not) and the words of every other Founder listed here.
Next: George Washington's 1783 Circular to the States. Note, this document was not written in GW's hand, but in that of an aid. GW signed it though. This address is only one of two places in either his public OR private writings where Washington mentions Jesus by name OR person. Some scholars therefore conclude the following as not characteristically Washingtonian. I disagree and conclude this was characteristic of the age.
The foundation of our Empire was not laid in the gloomy age of Ignorance and Superstition, but at an Epocha when the rights of mankind were better understood and more clearly defined, than at any former period, the researches of the human mind, after social happiness, have been carried to a great extent, the Treasures of knowledge, acquired by the labours of Philosophers, Sages and Legislatures, through a long succession of years, are laid open for our use, and their collected wisdom may be happily applied in the Establishment of our forms of Government; the free cultivation of Letters, the unbounded extension of Commerce, the progressive refinement of Manners, the growing liberality of sentiment, and above all, the pure and benign light of Revelation, have had a meliorating influence on mankind and increased the blessings of Society. [Bold mine.]
Again note how "revelation" is qualified with enlightenment terms, "pure and benign light." Some argue this address evinces that Washington believed the Bible -- harsh results and all -- trumped enlightened reason. But that is wrong. Were that so those enlightenment qualifiers would not have been used.
I understand why skeptical scholars deem Washington's Circular to the States -- written for public consumption -- to be an outlier: An aid wrote it and Washington almost never discussed either Jesus (by name OR person) OR his thoughts on revelation/the Bible. But this document endorses a decidedly enlightenment understanding of both. Though Jesus is spoken of as "divine," such categorization is consistent with not only Trinitarianism, but also Arianism (which views Jesus as a divine but created and subordinate being to God the Father) and perhaps Socinianism (which views Jesus as 100% man, not divine at all in his personal attributes, but on a divine mission). Indeed the enlightenment Arian thinker Richard Price enthusiastically endorsed this document when he wrote that he was "animated more than he can well express by General Washington's excellent circular letter to the united states."
Next, John Adams:
I really wish the Jews again in Judea an independent nation. For as I believe the most enlightened men of it have participated in the amelioration of the philosophy of the age, once restored to an independent government & no longer persecuted they would soon wear away some of the asperities and peculiarities of their character [and] possibly in time become liberal unitarian Christians for your Jehovah is our Jehovah & your God of Abraham Isaac & Jacob is our God.
-- John Adams to Mordecai Noah, March 15, 1819.
Note how Adams qualifies Christianity with "liberal" and "unitarian" as he champions "enlightened men."
Next, Ben Franklin:
That bodies should be lent us, while they can afford us pleasure, assist us in acquiring knowledge, or doing good to our fellow creatures, is a kind and benevolent act of God - when they become unfit for these purposes and afford us pain instead of pleasure-instead of an aid, become an incumbrance and answer none of the intentions for which they were given, it is equally kind and benevolent that a way is provided by which we may get rid of them. Death is that way. We ourselves prudently choose a partial death. In some cases a mangled painful limb, which cannot be restored, we willingly cut off. He who plucks out a tooth, parts with it freely since the pain goes with it, and he that quits the whole body, parts at once with all pains and possibilities of pains and diseases it was liable to, or capable of making him suffer. [Bold mine.]
-- To Elizabeth Hubbart, 1756.
Kind of a neat view of God. Though Franklin identifies life's purpose as "acquiring knowledge," "doing good to our fellow creatures" and enjoying God's kindness and benevolence, as opposed to embracing orthodox doctrines (the infinite sacrifice of Christ's atonement).
For James Madison, I am going to quote his address to the Cherokee Indians, "To My Red Children," August 1812:
"The Great Spirit has given you, like your white brethren, good heads to contrive, and strong arms, and active bodies. Use them like your white brethren of the eighteen fires, and like them, your little sparks will grow into great fires. You will be well fed, dwell in good houses, and enjoy the happiness for which you, like them, were created. These are the words of your father to his red children. The Great Spirit who is the father of us all, approves them. Let them pass through the ear in to the heart. Carry them home to your people; and as long as you remember this visit to your father of the eighteen fires, remember these are his last and best words to you!” [Bold mine.]
Note other above mentioned key Founders referred to God as "The Great Spirit" when addressing unconverted Native Americans. This is important because most orthodox regard the Natives' "Great Spirit" as a false pagan God. Madison's address also seemingly contradicts Trinitarian theology: Madison (reputed to be a theological unitarian) equated the "Great Spirit" with the Father. Some have argued the "Great Spirit" might be the Holy Spirit (3rd person in the Trinity). However, in referring to the Great Spirit as the Father, Madison would be confusing the distinct personalities of the Trinity.
Also, as noted above, many orthodox believe that only saved-regenerate Christians are "children of God" and Madison refers to unconverted Natives as his "Red Children" and the "Great Spirit" as "the father of us all" intimating that they as Indians qua Indians are God's children.