Nothing you've mentioned here counters the fact that US can trace much of it's founding heritage back to Christian ideals, premises and concepts. I did not say all of the Founders were Christian; I said most laid claim to that label. Some were Deists, which is markedly different than Christianity.
I was hoping that the Treaty of Barbary would come up, because this is the most popular one that gets used in arguments like this. For a refutation, go no further than Yale's own School of Law:
http://www.yale.edu/lawweb/avalon/diplomacy/barbary/barmenu.htmCheck out the piece that points you to the section called "Note Regarding the Barlow Translation". I've included it here, but feel free to confirm things yourself.
NOTE REGARDING THE Barlow TRANSLATION
The translation first printed is that of Barlow as written in the original treaty book, including not only the twelve articles of the treaty proper, but also the receipt and the note mentioned, according to the Barlow translation, in Article 10. The signature of Barlow is copied as it occurs, but not his initials, which are on every page of the fourteen which is not signed. The Humphreys approval or confirmation follows the translation; but the other writings, in English and Spanish, in the original treaty book, are not printed with the translation but only in these notes.
It is to be remembered that the Barlow translation is that which was submitted to the Senate (American State Papers, Foreign Relations, II, 18-19) and which is printed in the Statutes at Large and in treaty collections generally; it is that English text which in the United States has always been deemed the text of the treaty.
As even a casual examination of the annotated translation of 1930 shows, the Barlow translation is at best a poor attempt at a paraphrase or summary of the sense of the Arabic; and even as such its defects throughout are obvious and glaring. Most extraordinary (and wholly unexplained) is the fact that Article 11 of the Barlow translation, with its famous phrase, "the government of the United States of America is not in any sense founded on the Christian Religion," does not exist at all. There is no Article 11. The Arabic text which is between Articles 10 and 12 is in form a letter, crude and flamboyant and withal quite unimportant, from the Dey of Algiers to the Pasha of Tripoli. How that script came to be written and to be regarded, as in the Barlow translation, as Article 11 of the treaty as there written, is a mystery and seemingly must remain so. Nothing in the diplomatic correspondence of the time throws any light whatever on the point 
