Absolutely! I (sorta) made an entire post on this in regards to my love of classical music. I'm not going to repeat it or do it all over again, but I used to dislike classical music. Turns out I only disliked most classical and romantic era classical music, and loved medieval classical and 20th century and beyond classical. After loving those, I found it easier to even like the classical I hated.
I had a similar disdain for hip-hop. As a child, it was the only thing I listened to, since my sister listened to a lot of TRL and MTV. After being introduced to Ozzy Osburne's Blizzard of Ozz, I turned back on hip-hop and never looked back... Or so I thought. Call it my horrid introspection, but I like to revisit things a lot. I give things second, third or even tenth chances hoping I was mistaken before. One day someone was arguing over the artistic merit of hip-hop and this lead me to search for hip-hop I could like, if I could like any. I found these:
(^ This one really deserves a listen)
At this point, I'll stop, because I'm pretty sure you can figure out that my opinion on whether hip-hop is an artistic medium is: "uh, duh." There's a lot of good hip-hop out there!
So, I think you can learn to like music you previously disliked. Another example is my love for crazy classical music like this:
If you were to ask me what I get out of listening to music like this, I couldn't really tell you. At a first listen through, I stopped in like two minutes, and the more I listened to it, the more I grew to appreciate it until I really like it. What I can say is perhaps the sounds are really fascinating. It's quite interesting to hear them since I have never heard sounds like it anywhere else. You can hear similar sounds in small doses, but nothing like what you hear in that video... It's strange and awesome.