And before you start giving me the hooey about that referring only to the different Christian denominations, you should go back and read the actual debates about the clause. The founders were quite clear that even 'Mohametans' and 'Gintoos' were eligible for public office.
You need to read the debates on the First Amendment.
They made it clear only a national religion was prohibited.
You need to read the founders. They said it was the best thing for voters to prefer Christians as rulers...not to put that in law, but for the voters to decide.