Founding Father Benjamin Rush sometime in his life converted from Calvinism to Arminianism, and then to theological universalism, believing all would eventually be saved, after a long period of temporary punishment for non-Christians. As he wrote in "Travels through Life," his autobiography:
At Dr. Finley's school, I was more fully instructed in those principles by means of the Westminster catechism. I retained them without any affection for them until about the year 1780. I then read for the first time Fletcher's controversy with the Calvinists, in favor of the universality of the atonement. This prepared my mind to admit the doctrine of universal salvation, which was then preached in our city by the Rev. Mr. Winchester. It embraced and reconciled my ancient Calvinistical and my newly adopted Arminian principles. From that time I have never doubted upon the subject of the salvation of all men. My conviction of the truth of this doctrine was derived from reading the works of Stonehouse, Seigvolk, White, Chauncey and Winchester, and afterwards from an attentive perusal of the Scriptures. I always admitted with each of those authors future punishment, and of long duration.
As far as I can tell Rush's universalism was Trinitarian and consequently Christian. That is, it embraced Christ's work on the Cross. Arminianism rejects the "L" in Calvinists' TULIP, which stands for "limited Atonement" or that Christ only died for the elect. Though most Arminians may have retained their belief in eternal damnation, a common Calvinist critique of Arminianism is that if Christ died for all, not just His elect, then logic dictates that everyone indeed would be saved, which is exactly what Rush believed.
America's key Founders [Washington, Adams, Jefferson, Madison, and Franklin] because they did not believe in Christ's "work" on the cross, arguably don't merit the label "Christian" (even if they understood themselves to be "Christian" in some sense). Here is John Adams, who called himself a "liberal unitarian Christian," on the notion that an infinite God made an infinite Atonement for man's sins.
An incarnate God!!! An eternal, self-existent, omnipresent omniscient Author of this stupendous Universe, suffering on a Cross!!! My Soul starts with horror, at the Idea, and it has stupified the Christian World. It has been the Source of almost all of the Corruptions of Christianity.
-- John Adams to John Quincy Adams, March 28, 1816
Rush, though a Christian, also flirted with the theistic rationalist belief that all world religions were valid and could therefore support republican government. The content of "sound religion," according to the theistic rationalists, was that it taught a future state of rewards and punishments. And they explicitly included faiths outside the "Judeo-Christian" tradition in this formula. As Rush put it:
Such is my veneration for every religion that reveals the attributes of the Deity, or a future state of rewards and punishments, that I had rather see the opinions of Confucius or Mahomed inculcated upon our youth, than see them grow up wholly devoid of a system of religious principles. But the religion I mean to recommend in this place, is that of the New Testament.
Why would one venerate a "false religion" like Islam or Confucianism if they lead folks to perdition? Given that Rush disbelieved in eternal damnation, perhaps he reasoned the social benefits of belief in a false religion that taught the existence of a "Deity, or a future state of rewards and punishments" outweighed the cost of temporary punishment in the afterlife.
Rush's comments also illustrate how many folks tried to fuse the Christian religion with the principles of republicanism. As he wrote:
It is foreign to my purpose to hint at the arguments which establish the truth of the Christian revelation. My only business is to declare, that all its doctrines and precepts are calculated to promote the happiness of society, and the safety and well being of civil government. A Christian cannot fail of being a republican. The history of the creation of man, and of the relation of our species to each other by birth, which is recorded in the Old Testament, is the best refutation that can be given to the divine right of kings, and the strongest argument that can be used in favor of the original and natural equality of all mankind. A Christian, I say again, cannot fail of being a republican, for every precept of the Gospel inculcates those degrees of humility, self-denial, and brotherly kindness, which are directly opposed to the pride of monarchy and the pageantry of a court. A Christian cannot fail of being useful to the republic, for his religion teacheth him, that no man "liveth to himself." And lastly, a Christian cannot fail of being wholly inoffensive, for his religion teacheth him, in all things to do to others what he would wish, in like circumstances, they should do to him.
Rush's assertions I think illustrate the danger in government seeking to use religion for civil ends. Such risks corrupting the purity of orthodox religion. We've already seen Rush arguably do this in denying eternal damnation and venerating what orthodox Christians consider "false religions" which lead people to perdition. Clearly, republicanism as articulated by 18th Century American Whigs did not spring from the orthodox Christian religion or the Bible. And attempts to make it seem as though it did, no matter how useful politically, still distorts the traditional Christian religion into something it isn't. See for instance Samuel Langdon's sermon absurdly declaring that the Ancient Jews had a "republic," when in reality, they had a theocracy.
Though perhaps we can salvage Rush's sentiments by noting the compatibility between Christianity and republicanism. The historical record, however, is replete with traditional orthodox Christian who were anything but "republicans."
As Mark Noll et al. have pointed out one, of the worst abuses of the Christian religion by those arguing on behalf of America's Revolution was the way in which the Whigs argued that not only was God on their side, but Tories were not good Christians. I'm sorry, but England at that time was on balance about as "Christian" culturally or demographically as was America, but because they had an established Christian Church was formally a "Christian Nation" in a way that America was not. King George III was referred to as "His Christian Majesty." About 1/3 of the American population, including churches, remained Tory loyalists, on the side of the British. And their scriptural case based on Romans 13 was just as sound as the Whig interpretation, perhaps sounder. Moreover, some of the most notable "Whig preachers" arguing Romans 13 justified political rebellion were theological unitarians and universalists, like Mayhew, Chauncy, West, and Howard who used very unorthodox biblical hermeneutics to argue their points and fused their sermons with non-biblical Lockean state of nature/social contract teachings.
Not that loyalists were without imperfections -- I hate tyrannical government as much as the next guy -- but it insults the many American Christian loyalists, like George Washington's childhood friend Bryan Fairfax, to suggest their loyalty to Britain somehow reflected badly on their Christianity. The historic standards of orthodoxy in which the Christian religion is understood had little if anything to do with the conflict between America and Great Britain in 1776 or the consequent construction of the Constitution. Jesus did not abolish one social institution; not tyrannical government, not slavery, not one. Christians looking to the Bible on matters such as the American Revolution or Civil War have to look elsewhere, otherwise they engage in novel, self-serving, "convenient" readings. And this is what Benjamin Rush did when he attempted to fuse Christianity with republicanism.