Are you really willing to bite that bullet? What if the person was a member of an anti-vaccination group? Or a racist group?
My answer to your question is, "It depends." because really it does depend on a lot of other things, such as how many other comparable candidates there are. Given typical circumstances, I draw the line just before enthusiastic religious belief, like in my hypothetical. If it was an easy decision, I wouldn't be posting about it.
What if the person was a member of an anti-vaccination group? Or a racist group?
This person is sending very bad signals about himself, signals most people will not ignore. But they don't actually say anything about his job performance (in this hypothetical case)!
Incredible, I'm very lucky he is probably severely undervalued in the labour market. By hiring him I am getting a bargain.
I attach no metaphysical badness to him getting paid by me because a boycott on hiring people who use their money for ill is impossible to enforce. Someone else will profit ...
Let's say you are interviewing a candidate for a job. In casual conversation, the candidate mentions that he is a member of a rather old and prestigious country club. You've never heard the name of the club before.
You look up the country club afterwards, and are surprised by what you read. The club refuses membership to homosexuals. It revokes the membership of couples who use birth control. Leadership positions are reserved to unmarried males.
The candidate is otherwise competent. Under what conditions would you hire him? Would you want a law passed banning hiring discrimination based on country club membership?
(The country club is analogous to a nicer version of the Catholic church. I left out a couple bad things.)
Religious discrimination is illegal in many parts of the world, and I think that's probably a good thing. Still, keeping this at the object level (no meta-rules or veils of ignorance) it seems to me that discriminating against religious people is fine. I'm curious what other people think.