The nature versus nurture debate has been going on in the sciences for well over100 years. I doubt a final conclusion has been reached.
For most of the people I know, the music they most often like ties back to what they heard in their childhood and teenage years as they were developing. I know my parents didn't care for the Beatles and their many cohorts who became famous in my early teens, but they loved Big Band music which was the hot thing when they were young.
As a side story, I ordered by phone from a local hole-in-the-wall Chinese restaurant earlier this week. The owner's wife who answered the phone asked me to wait for a minute. She didn't put me on hold so I heard what was going on. She began to sing to herself -- a Chinese song that apparently she really liked. The words obviously didn't mean anything to me, but the melody also did nothing for me -- I couldn't envision anyone who thought that was a catchy tune. But, then I didn't grow up in China.
Cast my vote for a heavy dose of nurture.