Yeah IMO Democrats definitely listen to a wider variety of music. I don't even know how you could argue otherwise.
I think Republicans, because "genre purists" who refuse to listen to almost anything else tend to be liberal-leaning.
I think you're maybe jumping to conclusions based on your own experiences.
You don't think "classical music snobs" aren't overwhelmingly Democrats? If nothing else they're heavily clustered in urban areas (that's where the symphony halls are), in addition to being highly educated.
Classical fans have gotten heavily Democrat since the arrival of Trump on the political scene. The correspondence of affluence, age, and whiteness would have made it actually a lean R demographic, in the grand ole times.