In my opinion, nations are not religious. The leaders and the people of a nation may belong to one religion or another, and they may govern by principles according to their religion(s), but the nation itself does not belong to a particular religion.
On another line of thought, each of the early colonies came here to practice their particular brand of religion free from whatever interference that they had received in their homelands. But to the best of my knowledge, none of the early colonies practiced what we would call “freedom of religion”. They came here to be free to practice their own religion, but they were not interested in allowing others to practice a different religion within their colony.
By the time of the revolution, this had changed in some of the colonies, but several of the thirteen original states still had official state religions even after the passage of the Bill of Rights and its guarantee of what we now call “freedom of religion”.
This alone should tell you whether the constitution was intended to apply to the states as well as the nation.
True enough Puritans came here to escape official Anglican dictat, and Catholics from England came here to escape both, but there was a lot less of that than is popularly imagined.
America was a tough place to live ~ people struggled to survive ~ many early settlements had a single building used by several religious bodies ~ even those whose members didn't intermarry or socialize ~ try looking up OLD YELLOW CHURCH ~ there are several of them. Everybody went there.