Artists who's music you love, but who's politics you hate. Bruce Springsteen, Neil Young,& Pearl Jam to name a few. I love their music, absolutely hate their political views.
Linda Ronstadt.
I can say the opposite of the question from the OP. An artist who's music I was never too crazy about but who's politics I agree with is Melanie. My mom used to play her records sometimes when I was a kid and while I never liked many of the songs, one I don't mind is "Lay Down (Candles in the Rain)".