I don't think politics/religion has ever been a huge factor in my games. Now, my degree is in political science and philosophy, so you know it's not because I don't have opinions. I just think that it's more because two people can disagree strongly about something, but still respect one another. It's the difference between "fraternizing with the enemy" and "the loyal opposition".
In my current group, there is a socialist and extreme capitalist (if you know which I am, great, but not relavent). We've had political conversations, and butted heads on a couple of things. We don't talk politics much anymore, but I think that's mainly because we've been there and done that. We're both general decent people who hold our beliefs because we genuinely believe they are the best for everyone involved. Understanding that goes a long way toward being friendly. In fact, I'd rather call someone on the other side of the fence, but generally decent, a friend than someone who agreed with my politics, but did so for selfish or bullheaded reasons.
Maybe therein lies your issue, too.