That person appreciates good music.
appreciate: 1. transitive verb If you appreciate something, for example, a piece of music or good food, you like it because you recognize its good
"Anyone can appreciate our music." (Collins Dictionary)
You could also say that the person has eclectic taste or even that the person is an eclectic (using the word as a noun).
eclectic: (adjective) eclectic 1.deriving ideas, style, or taste from a broad and diverse range of sources. "her musical tastes are
A person who derives ideas, style, or taste from a broad and diverse
range of sources. (Oxford)
Example sentences also from Oxford:
‘But they are not just reactionary eclectics; they think they can twist and recombine architectural history in fresh and original ways that would have been unthinkable before modernism wiped the slate clean.’
‘Douglas is the king of jazz's current crop of eclectics: He's the kind of guy who shows up at a Jewish wedding with a tango band and proceeds to play Bjork covers.’
‘The two strongest objections each approach levels at the other is the claim that eclectics are undisciplined, and that traditionalists are stagnated.’