"I know that I'd have to think seriously about voting for any politician who states that he will follow the dictates of his religion's prelate in matters of public policy"
The implication is that you wouldn't think seriously about voting for someone who follows an unknown or changing philosophy that can't be researched? That would be fine? But someone who is religious, you gotta check them out real close? That's anti-religious. If you care about the Catholic candidate's opposition to handing out contraceptives to kids, for example, you should also care where his opponent stands on the issue. Otherwise you're just scared of, biased against (etc.) religious people.
Obviously a candidate's philosophy is a major thing to vote on. But you're saying you'd need to closely scrutinize religious people in particular.
No, the topic just happens to be religious candidates. If a candidate said "I follow the precepts of Ayn Rand [or Karl Marx or fill in the blank]," then I'd equally want to find out what those precepts are.