I can listen to just about anything.
My parents were dating in the late 1940s, so my house growing up had lots of Big Band 78s (kids- ask your parents...or maybe grandparents) and 33s of Glen Miller, Tommy Dorsey, Duke Ellington, Louie Armstrong and the like. My mom also liked the "crooners", so add in Perry Como, Mel Torme and, of course, Francis Albert Sinatra.
They pretty much skipped the Fifties.
By the time I really began to get into music in the late 1970s, I had an embarassment of....well, if not exactly "riches", then at least "choices": you had disco, country rock, early New Wave and punk, rock (or "classic rock" as it is now called), rockabilly, hard rock (not "metal", not quite yet) and a few other genres. I listened to everything from David Bowie to ABBA during this time.
Still do.
High school came along, and I gravitated towards two genres which, together, made absolutely sense: British Invasion circa 1963 to 1968 or so and New Wave. If I had a IPOD back then, shuffle might produce something by The Beatles followed by something by Devo. Led Zeppelin might segue into Madness.
Once Grunge came out, I went straight to classic rock on my car radio and never looked back
These days, I love me my Sirius/XM satellite radio. I have presets for my 80s stuff, Rewind (which is cassette era stuff like Yes, Van Halen, etc.), Classic (little bit older stuff) and my favorite First Wave, which has all my New Wave and Punk favorites (Public Image, LTD, Psychedelic Furs, Yaz, Madness, Talking Heads, Depeche Mode and more) in one place. The app has the same ability as Pandora to allow you to upvote or downvote based on individual songs so it can provide a customized playlist.
I'm not a fan of much of what passes as "music" these days, especially what I'd say is the current iteration of "Top 40" or "Hits" radio. It all sounds pretty much the same to me, what with vocoders to hide just how bad a singer you really are and synthesizers meant to cover up just how bad a musician you are. I still can't get into classic country, but at least I respect the talents. Rap I do not even consider "music", nor do I think the 'artists' talented in the least. But hey....I doubt fans of rap would dig The Alarm either.