The below video from Mike Slater features a couple of relevant clips from Voddie Baucham and two substantive interviews. It is instructive and is worth watching:
Constitutional Conservatism and Biblical Christianity in the Piedmont Triad of North Carolina
Would a Christian nation kill millions of INNOCENT PEOPLE as the US has done in the Middle East for Israel, which is pretty anti-Christian?
Christianity was a major positive influence on the culture that produced the founding. But Deism was really in vogue ~1776 (at least briefly) and seriously contributed to religious freedom and the emphasis on individual rights. Jefferson, Franklin, Thomas Payne, NC’s Willie Jones, and others were Deists. John and Abigail Adams leaned that way. Washington refused to take communion. (Of course, it should be said that Deists weren’t exactly anti-Christian, just rejecting more mystical aspects of it. And I also have the impression that some who toyed with Deism as they graduated from Princeton ~ 1776 went back towards conventional Christianity by the 1790s.)
The Founders were obviously a bit less Christian than the monarchies of Europe, which used Christianity as the very justification for their forms of government…which forced its subjects to pay for churches and taxed them extra for not attending. They were very seriously Christian.
In response to your first question, J. Sobran, no, they would not. There are a couple of complicating factors. Theology within certain sectors of Christianity got hijacked by the Zionist cause; and that influenced many Christians. In addition, the Islamists and Middle Easterners often did just enough to hurt us and/or provoke us for American Christians to rationalize getting involved.
With respect to both of your comments, yes, Deism was “a thing” back then. I am not sure that it was as pervasive or as dispositive as you seem to suggest. If we did a study of many of those names listed, we would find the truth is a bit more complicated. But there is no question that Christianity heavily informed the founding, and that the colonies at that time were overwhelmingly Christian.
Ethan Allen, James Madison, and James Monroe were also Deists. I think Nathaniel Macon was Deist was coming out of college (the Founding period) but became more conventionally Christian later in life.
A lot of the good Christianity contributed to the Founding had to do with the particular strain of Christianity that existed in America, informed by the tolerance of the Quakers and of John Locke (not the intolerant Puritanism of New England, Anglicanism of England, or Catholicism of France–all of which supported a serious degree of tyranny of authority over the individual).