If you can't get into a band because the lyrics promote things you're diametrically opposed to, that's reasonable enough. If you dislike a certain belief or worldview enough, listening to it constantly likely isn't your favorite past time.
There is no reason, though, to be completely repulsed by an artist's output simply because the artist has a belief or stance outside of his/her art that doesn't fit your worldview.
Art is art. The source doesn't matter unless you let it matter. It's up to you and how you choose to consume it. Enjoying the creative output of a musician who's religious, areligious, homophobic, vegan, racist, sexist, anarchist, socialist, libertarian, polygamist, thieving, molesting, murdering, or a WOW player doesn't spread that position unless the song you like is propaganda, and even then, if you're a reasonable adult, you can probably listen to it on your own without suddenly changing your stance to that one.