That's why they did the service fee thing. One of my ex-coworkers quit the union because they supported pro choice candidates. When she was disciplined for some seriously bad things, she was still represented by the union because she paid that fee. The reason she "was allowed to resign" had nothing to do with her union membership and everything to do with fraud.
My union does not represent any side in arguments between one member and another. Management are not members of my union, from my first-line supervisor all the way up. Some of them have their own union (I think), but it is small and not the same as mine (UAW-again, I don't think we should be allowed to have the UAW represent us, because they give money to political campaigns).