If it does become a problem, one thing I'm considering is using voting behavior as a way to try and identify and ban "false-flaggers". So if a user has classified themselves as left-leaning, but their voting behavior and the way other users vote on their posts/comments looks a lot like a right-leaning user, they could be banned or forced to change groups.
Plus, what we think we are is a bit problematic these days. The extremes of both sides of the scale take up some of the room we thought we had on the sides. If you are honest with yourself, there is a lot of self examination going on.
Even if you haven't changed, things around you have. Hell, relatives I once supported have sold their integrity and feel justified in it, but I have had my own questioned because of them. Its just a weird world.
As to the site, the default front page was basically all "left" outlets when I looked. If you actually want both sides to compare, then you probably need to look at source as much as people.
Looking back at past threads, dragonwriter and myself don't agree often, so take it for what its worth.