This question has made me think. I mean, I really do seem to be a better, happier person with more (and more diverse) friends when I avoid political discussions. I think a really big part of this is that I really enjoy being around people who are different from me. People who are good at different things; people who come from different backgrounds. (I mean, with some exceptions. I have prejudices, like everyone else. I'm working on it.) And these people, usually, have very different political and religious ideas than I do.
I mean, for example, I think having religion and going to church, in general, is no better (or worse) than, uh, religiously attending your favourite animé convention, and participating in con politics. I mean, both seem a little weird in my mind, but I have many friends who are deeply and genuinely religious, and many friends who regularly attend animé conventions. (really, I have little more than "Boy, that's... different" curiosity when it comes to religion or animé conventions.) I'd really rather keep both sets of friends. And you know what? If I keep bringing this up to my religious friends, they probably aren't going to want to be around me (just like if they kept trying to convert me, I probably wouldn't want to be around them.) I mean, I don't hide my non-belief, but I try to largely avoid the subject, and when it does come up, I try to be respectful, and ask they do the same for me.
Really, there are many areas of politics that are, if not directly religious in nature, are still taken on 'faith' -
For example, some people feel that society has a responsibility to take care of all of the less fortunate. Nobody should starve in the street or lack for basic medical care, regardless of what poor choices they made. Others feel that if society gives everyone a fair shake, their responsibility is met. Those who chose well should not be forced to support those who chose poorly.
Now, most people believe something between those two viewpoints... but it's fundamentally an emotional choice. Sure, you can argue the merits of a particular policy on logical grounds, but that is a mere implementation. the base question I gave as the example can really only be answered on an emotional level.