Two of those matter. The third doesn't.
Two of those are political positions, one is a personal preference. I couldn't give a crap if a man wore a dress if he represented my interest in politics.
And that's kind of how the system is supposed to work? We are supposed to be a meritocratic democracy, where you get elected based on your skills and your politics, not on personal things.
Part of what people believe is a "merit" for a potential elected official is their character. People's character can be measured in many ways (given around 310,000,000 people in the United States I'd say that on any given day there are 350,000,000 different definitions of what can be used to measure a person's character
), and what the candidate's moral beliefs are will be used as a part of probably over 200,000,000 of those definitions (my personal rough guess - I have no link to a study or anything). This is why Kennedy was questioned about whether or not he'd follow the Pope or the Constitution (he sucked in many ways as a president, but certainly not because of his Catholic belief system). Far fewer questioned Romney on being a member of the LDS faith, which I find good because it means people are moving away from using religion as a guide to elected officials.
However, if you knew someone believed, actually believed there is such a thing as the FSM, would you elect that person? What if they actively sought to make Intelligent Design a part of school curriculum next to evolution? Would you feel the same that their religious beliefs don't matter? My guess is that you would not want a person putting Intelligent Design into the curriculum of your kids' school, because you disagree with that on a fundamental basis. If not you personally, you could understand other atheists being against it. For the average voter, it's the same in reverse - we don't want a Bill Clinton-esque cheater, because that moral value system is inconsistent with ours. How does that affect his ability to be a good leader? It may or may not, but it does affect people's perception of his ability to be loyal to the country, to his job. "If he promises before God, family, and friends to not cheat on his wife and then he does approximately 16 times a day over the course of decades, how faithful is he going to be to his oath of office?" is what people ask themselves.
So, yeah, actually, all three of those things matter.
