Few years ago I talked on a forum about disagreeing with the lyrics of a Ramnstein song, a band I used to listen (right now I don't listen to Ramnstein not because of the lyrics, just because recently I'm more into Death Metal).
This user told me that she only reads stories and listen to music which messages and texts suit her vision, because to her, message come first, art later.
Instead I enjoy music and stories beside the message. For example I was and I am definitely right winged, and as teenager not only I listened to punk music that was filled with anarchic and left winged lyrics, I even sang them while listening to music, even if I did disagree whit what they say.
Right now I listen to Amon Amarth music a lot. I often disagree when Johan speaks against Christianity, but I enjoy their songs. As long as people don't do antisemitic and/or jihadist propaganda (therefore yes, I would avoid that), I'm fine.
Another thing - and this is related to my art - a thing I often find irritating is when an authors get in the story, and it happens often. For exampe an author is a misantrope, and is known to said: 'I would like to be a wolf rather than an human'. And one day, when you read a story, his main character, or one character he enjoy most, express the very same hate toward humans, and at certain point he sais exactly: 'I would like to be a wolf rather than an human'. The reader notices that the character was created right after the author, and that the words aren't of the character, but they are from the author himself.
(I still remember how Miyazaki exaggerated in Momomoke princess, and made the wolves appear worse than the humans they hated).
Is also true that to me, moving characters that are different (not the opposite, or you go to the other extreme) from me is way funnier. I have to see things from different perspectives.
I think listening to music and reading books that share messages that don't suits my values help to keep your mind more open, but still, the main reason is: Why deny myself from music of Amon Amarth(example) that I love just because I'm not on the same page with Johan?
Why giving up to read Terry Pratchett books because in his book very often he shared ideas that are very different from mine?
Listening to: Amon Amarth
Watching: Dragon Ball Super