Mixing politics and music can make music seems relevant and important for the period in which it was written. In that respect, it can support social change and and give voice to things people feel but can’t put into words.
But generally that also makes them irrelevant a few years later. "Ohio" by CSN crystallized a moment, but it doesn’t even get played on the radio anymore and people under the age of 60 have never and will never listen to it..
Contrasted to musicians who are vocal about their politics outside of their work; it doesn’t make sense, musicians have no insight greater than any other people about politics, and you just alienate half your audience.
Consider the reason people still listen to Mozart, Beethoven, Schubert and a small set of musicians hundreds of years after they’re dead. People still listen because the music is good. Whatever politics they had or their works represent is largely irrelevant to why we still listen to them.