My tastes have shifted somewhat over different time periods, as I'll focus more on one genre for a while, then another, but overall my tastes have always been wide-ranging and eclectic.
If you are speaking of "new" or "modern" music as ONLY what the mainstream industry giants want to force-feed down your ear-pipes, people like Beyonce and Taylor Swift, then I don't like modern music, either. But in fact, there is a great deal of "new" music out there that is very good and worth listening to. You just have to seek it out for yourself, apart from the "mainstream" (I question whether it is really even that, any more) stuff.
I'm not terribly fond of rap/hip-hop, and never have been, although I understand and accept that it appeals to some people, and I do like a few individual songs from the genre. There were individual songs throughout the years that I disliked, too (Michael Jackson's "Ben" or Debbie Boone's "You Light Up My Life" can still send me screaming for the exits, hands pressed over my ears and babbling loudly to prevent myself from hearing them, almost

), but the ratio of "enjoy" to "can't stand" with the two groupings is roughly reversed. That's fine; we each have our own preferences.
Even as a little tacker in the sixties and a teenager in the seventies, though, I was into a LOT of stuff, from psychedelic and heavy metal and classic rock to 30's-40's big bands to opera (preferably live, which I love; opera recordings tend to bore me) to modern jazz to Native American (then called Indian) songs to Japanese shakuhachi and koto stuff to... you name it! I even liked (and yes, still do, he admits blushingly...) a few disco tunes, at least for dancing to.
I probably like less of the techno/rave stuff (although I like some of it very much) and even less of the rap/hip-hop stuff than any other genres. I don't care for a lot of the currently "mainstream" music, either, as I said above. Not that I DISlike it, I just don't particularly want to listen to it. (Some rap stuff I actually really dislike, though.)
Perhaps it's foolish of me to think this, but I'd like to think that my tastes would be largely the same, even if I had been born thirty years later. Like a few youngsters today, I think that I would tend to like and dislike much the same things that I do, and have, but would also go through "phases" or periods of liking one a bit more, than another. I've done that all my life, and don't expect it to change.
Music to me is almost like a drug, but one for the emotions. If you are angry or stressed, put on the right songs, and after a while all is right with the world again. What those songs are may vary from time to time and from one emotion to another, but I suspect we all choose music based on what mood we are in, how we are feeling at that moment. It's our brains telling us what drug we want at that particular time, and as we change with our environments and times, and with our health and our age, those choices change, too. My brain has always been wide-ranging and chameleonic to some degree, so it seeks a wide range of drugs. I'm rarely into mindless aggression, which (flame suit on) is largely what rap and hip-hop are aimed at and fit best with, so I largely don't like it. I don't think that would be very much different, no matter when I was born, especially since at one time or another, I like or have liked almost everything else (at least genre-wise; most individual songs I dislike I continue to dislike) --just not all at the same time!