As I noted in this comment thread at Volokh, someone argued on behalf of America's "Judeo-Christian" heritage. We certainly have something that could be called a "Judeo-Christian" heritage but also have:
a) an Enlightenment heritage; b) a noble pagan Greco-Roman heritage; c) a freethinking, religiously inclusive and pluralistic heritage, one that tolerates, indeed sometimes celebrates heresy and dissent in dominant religious movements; and d) an ugly illiberal heritage along with it that violated the liberty and equality rights of women, blacks, religious minorities and so on and so forth.
And btw, Jews and Roman Catholics were often the victims of d).
And we might also want to think the "cool guys" aren't part of d). No the freethinking liberals of their time engaged in d). Jefferson has some embarrassingly racist stuff in Notes on the State of Virginia. The liberal unitarian Christian John Adams was an anti-Roman Catholic bigot and so on and so forth.
But remember too, the orthodox forces of religious correctness engaged in d) as well. As one of them put it arguing against the "No Religious Tests" clause in the US Constitution:
An anti-constitutional article written for the New York Daily Advertiser that same January and widely reprinted within days in Connecticut, New Hampshire, and Massachusetts papers pulled no punches about the social repercussions of Article 6. No religious tests admitted to national lawmaking: "Ist. Quakers, who will make the blacks saucy, and at the same time deprive us of the means of defence--2dly. Mahometans, who ridicule the doctrine of the Trinity--3dly. Deists, abominable wretches--4thly. Negroes, the seed of Cain--Sthly. Beggars, who when set on horse back will ride to the devil--6thly. Jews etc. etc." Not quite finished with the last, the newspaper writer feared that since the Constitution stupidly gave command of the whole militia to the president, "should he hereafter be a Jew, our dear posterity may be ordered to rebuild Jerusalem."
Source of Information:
The Godless Constitution, The Case Against Religious Correctness. By Isaac Kramnick and R. Laurence Moore. W. W. Norton & Company New York/London.(1996) pp 33