How about people just stop talking about politics at work? If it isn't germane to your job and isn't pleasantries like talking about your weekend or your hobbies or moving or your kids or whatever, just leave it at home. It's just like dating coworkers: sure, it might not be expressly forbidden by office policy, but does that mean it's a good idea?
Oh wow, who knew it was that easy! Why didn't anyone think of that? I'm glad you've single-handedly solved the problem.