The Treaty of Tripoli is oft used, perhaps 'misused' in debates on this point.
Originally Posted by beefheart
Many contend, with reason, the language was put in/massaged to reassure the Muslim Nations that we weren't in a religious war with them.
Wiki continues on that point/Article 11, beyond your short excerpt:
Treaty of Tripoli - Wikipedia, the free encyclopedia
Article 11 ...
According to Frank Lambert, Professor of History at Purdue University, the assurances in Article 11 were "intended to allay the fears of the Muslim state by insisting that religion would not govern how the treaty was interpreted and enforced..."
"..At least one member of Adams' cabinet, Secretary of War James McHenry, is known to have protested the language of article 11, before its ratification.
A second treaty, the Treaty of Peace and Amity signed on July 4, 1805, superseded the 1796 treaty. The 1805 treaty did Not contain the phrase "not, in any sense, founded on the Christian religion."
Again, I'm an Atheist, this is a Matter of history and true characterization of this country I am proud has the heritage it does.
It was the Christian Nations/conscience (UK, France, USA) which brought the principles of democracy and individual rights/freedom to the modern world.