I agree with both of your points, and I was born in 1979. My dad was into the music of the 60s, like Jethro Tull, The Doors, Led Zeppelin, and Pink Floyd. My mom was huge into the Beatles. I love all of the above mentioned bands, and while I listen to more metal than anything, the metal I love definitely take elements from all of the above, along with Black Sabbath. Now you need to really dig to find what you enjoy, it usually won't show up on radio, or even on a related Spotify playlist unless you make sure to constantly interact with and like music you are into.

Hip-hop and rap seem to be more divisive for boomers (not using the term as an insult, my parents are both boomers, who I respect), and I think it's more because the message was more in your face and violent (as far as what was publicized). There is a lot of hip-hop and rap that is much more socially conscious and aware from the 90s up to today, that aligns more with the messages from the 60s. I enjoy both, but I have gotten my dad into groups like the Beastie Boys and Cypress Hill/Wu-Tang Clan, while skipping over the tracks that I don't think he'd enjoy. I think it's fine to not like certain styles of music.

I don't enjoy modern country at all, but I like Bluegrass and Americana type music, with my favorite Grateful Dead album being Workingman's Dead (arguably quite a bit different from the rest of their catalog). You just have to search more for what you like now than in the past where you really could find good music on public radio.