I think it's a question of time.    You can probably teach yourself to appeciate any number of genres--but it might not be worth the trouble.

I have to say I was curious about the current top 40, so I listened to the whole list at the end of the year a few years ago.    It was, sorry to say. a hard task.    I'm afraid I don't want to dedicate any more time to any of that stuff. Not even tempted--though there's a relatively recent group called Train which has some wonderful stuff (maybe since they have a wicked sense of humor, which hugely raises any kind of music in my book).

I love--passionately in fact--a long list of types of music, including orchestral, chamber, jazz, country, bluegrass, doo-wop, other early rock, old counry, even some recent country (a lot of of Brad Paisley, some George Strait, some Miranda Lambert,   I think there are even a few Taylor Swift songs, though please don't make me swear to that), a lot of folk (except navel-gazing writers), some opera (though very few arias), Balkan, Sephardic, madrigals, Sacred Harp, sea chanteys, gospel, spirituals. And the list goes on. Not all of every type.    Hot jazz, rather than cool jazz, for instance.

I'm sorry for people who don't appreciate classical music, for instance, since I get so much pure joy and pleasure from lots of it.   But I think it's just the luck of the draw; I was lucky enough to grow in a house where I heard a lot of it.   

I'll have to admit the only rap song I really like is "Cicada Serenade", which ain't exaxtly the quintessential rap song. I wonder if you grow up listening to a lot of rap, is it really as wonderful experience as some of these other types.   I doubt it--subjects aren't really very uplifting, it seems--but who knows.

But life is too short to inflict music on yourself that you really can't stand.   If this be treason to the folkie ideal of tolerance, then make the most of it.