Would you be okay with a president being in office that was an atheist?
Sure, no problem with that at all. Same with being a Muslim, or whatever. Their personal beliefs are their personal beliefs - personal. When they swear in and become POTUS, I DGAF about their personal beliefs, those left consideration when they swore in. They now are a public figure with a public job of doing what is best for the country as a whole, their personal beliefs be damned.
Now, they have values that perhaps those beliefs are based off of, and that is where it gets sticky. Bush and stem cells again is a perfect example. And again I'd say they need to be highly careful of applying their values, based sometimes largely off their beliefs, to their actions as POTUS.
This IMO is why people just have such a distrust of Billary:
No one that has more than two working brain cells trusts anything that comes out of her mouth. She
may be speaking the actual unvarnished truth, or, she may not. She
may be twisting or embellishing or tweaking what is correct for her own benefit/goal, or she may not. People want a politician they can at least halfway trust what comes out of their mouth, who actually believes in something not because it gets them what the want/votes, but because they actually believe in it. This is why people like Bernie, because even though someone on the Right has large philosophical differences, Bernie is at least as genuine as you'll ever find in a Politician - he takes the P and replaces it with a p. Trump is the same way, except he's having to perform to get the far Right vote/support so he can get the nomination. Trump as POTUS would be much less disasterous than those on the Left believe.