John Dilulio, former head of the White House Office of Faith-Based and Community Initiatives, has a new book out called Godly Republic. I was leafing through it at the book store; it looks interesting and makes some valuable points. I find much common ground with his understanding, but also disagree with parts of it. He lauds Jon Meacham's book which rejects both the "secular state" and "Christian Nation" paradigms in favor of a more balanced middle way which Meacham terms "public religion," and Dilulio terms "Godly republic." He admits his analysis tilts to the right of Meacham's. My position is closer to Meacham's. I note, though Meacham disagrees with the term (because the concept was first put forth by Rousseau, who had less than pure motives for it) what he and Dilulio argue for is the founders' notion of "civil religion," which is not Christianity, but inclusive of it and other non-Christian theistic faiths.
Dilulio notes that this system is public endorsement of religious pluralism under God and that such pluralism extends beyond "Christian" religious systems, indeed even beyond "Judeo-Christianity," (he explicitly includes Islam). He wrongly, in my opinion, concludes this public God to be the God of Abraham. Allah, who is part of this public religion, claims to be the God of Abraham, but many orthodox Christians disagree. Further, the key founders -- Washington, Adams, Jefferson, Madison, and Franklin -- explicitly held other non-Judeo-Christian belief systems like Native American spirituality, pagan-Greco-Romanism, and Hinduism also part of the generic Providence worshipping public religion. And finally, the key founders believed only "parts" of the Bible were legitimately revealed. So their monotheistic God was perhaps the God of Abraham -- the God of Bible -- but with a meaningful caveat: Those parts of scripture which show what they deemed God's "irrational" attributes -- His wrath, jealously, excessive punishments and outlandish miracles -- were edited so that only God's "rational" attributes -- His benevolence, wisdom, goodness and power -- remained.
Ben Franklin sums up the lowest-common-denominator of America's public religion:
That there is one God, who made all things.
That he governs the world by his providence.
That he ought to be worshipped by adoration, prayer, and thanksgiving.
But that the most acceptable service to God is doing good to man.
That the soul is immortal.
And that God will certainly reward virtue and punish vice, either here or hereafter.
This is similar to what Avery Cardinal Dulles termed The Deist Minimum but perhaps better is understood as a "theist" minimum. Deists, as I understand their views, would agree with those 6-points, but ridicule and evidence hostility towards religious claims that go beyond them. (Some of the stricter Deists might have a problem with point 3.) Christians, on the other hand, would also agree with those 6-points, but would also note such creed to be woefully deficient in that it leaves out accepting Jesus as Lord and Savior and His Atonement as essential for salvation (indeed, this might cause Christians to have problems with point 4; Christians believe doing good for fellow man is laudable, but arguably it is not "the most acceptable service to God" -- accepting Jesus is). Theological unitarians/rational theists, on the other hand, strive to be friendly towards all religions -- orthodox or heterodox, Christian or not -- that (more or less) accept these 6-points. Indeed, Jefferson, Adams, and Franklin were so friendly towards various exotic world religions that they included systems like Hinduism, Native American Spirituality, and pagan-Greco-Romanism, as accepting the 6-point essentials of "sound religion," when one could plausibly argue they do not quite.
Atheists and agnostics are perhaps anathematized by this formula. And my personal position is they should be viewed as equal citizens with religious folk. The founders believed atheists should have full civil rights. I would go further and try to guarantee atheists or agnostics not feel anathematized by government endorsed religious messages. But this is where I differ with America's founders.