Politics, Religion, and other dangerous discussion topics tend to be polarizing in the sense one is ambivalent about them or its part of their core identity. Even when music is apolitical the artist in question is likely to have artistic & philosophical thoughts influenced by similar circles; and what is music if nothing else than one externalizing their own personality & interests?
To answer the question, I tend to dislike music whereas I disagree with the personal beliefs of the artists regardless the focus of the music. I do have exceptions sure, and no I don't know the people behind everything I listen to; however when I hear new music & proceed to look up the artists behind it I am usually correct as to their affiliations provided they're public. And I have abandoned albums I previously liked due to change in ideology on my side, especially in the case where I had a falling out with one of my favorite musicians.
Ironically as harsh as I sound here I'm more likely to spin apolitical music than political, I'm involved enough with politics as is.