It would have to change fairly little, I suspect, to accomadate a woman president. It wouldn't surprise anyone that much.
It would have to change quite a lot to accomodate a gay president.
Given the tensions between the cultures, I couldn't imagine a Muslim becoming president (though some, I suppose, attempt to claim Obama is one, but their claims are baseless and feeble) in the current society.
In principle, an atheist president should be non-noteworthy because the US was concieved of as, and is legally, a secular state. In reality, of course, it would be hugely noteworthy, but then again, US society would again have to change quite substantially before it happened.
Not sure there's more than a hair between the last three.
In principle, all those factors should be irrelevancies.