I don't think Batman can be easily categorized. Being a vigilante implies some measure of libertarianism. To back this up, he is also filthy rich and uses his wealth to compete in the superhero game, a league where he is otherwise unqualified to be. But he's delusional enough that I bet he actually believes he's doing good, and thus he probably votes Democrat.
FoC: He THINKS he's fighting corruption, but he's part of it. Holding such delusional beliefs, it's no wonder his politics are muddled.