I think, when done well, a discussion about politics or religion can be fascinating, enriching and possibly even change a person's entire perception on things, which is why I do think they have a place on discussion boards. It's the same reason I think pretty much any topic does, even if it covers a sensitive subject. If certain subjects that really matter to people are off limits in a community, it makes it much harder for those people to connect with others in that community on a deeper level.
However, I also realize that it's far too easy to fall into the trap of unnecessary hostility, callousness and overreaction in such threads. I don't think the answer isn't doing away with such threads as a whole, but establishing some guidelines for which a calm, friendly discussion can take place. I don't mean rules, but rather just a set of criteria that establishes what people consider good etiquette for having these conversations. I don't imagine it'll solve every problem. We all get overheated now and then. At the very least, though, it may be of some help to the people willing to try and follow it. I certainly like the people on here, and I've definitely seen some great conversations pop up on some rather deep topics. I wouldn't want the continuing potential for that to go away.
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