To have an absolute distaste for music is definitely not normal. We have a natural attraction to music, especially stuff like simple beats. That's why a lot of popular songs have a strong, catchy beat. I could see being really picky and generally dislike most music you come across, but that's different from categorically hating music. I'd actually expect something is physically or mentally wrong if you are actually incapable of enjoying music.
I can definitely see why some people wouldn't care to invest what many of us invest in set ups for listening to music, but I can't imagine why someone would spend any significant amount of money before realizing that it's not that important to them.
I agree with TheGhost, though I hadn't really specifically thought about it. I have 3 pairs of headphones and 1 pair arriving in the next day or 2. I'm planning on selling 1 pair that I already have, but ended up finding another pair I want. Since TheGhost mentioned it, I've now considered that maybe I should invest that money into some newer music or into some of my favorite stuff on vinyl. I'm a tech guy at heart, so I can get a bit carried away with the physical/hardware aspects of stuff and lose sight of the actual purpose. I find myself listening to a lot of the same stuff lately and expanding my music collection would probably be a smarter idea for me. Others, like TheGhost suggested, might be better off spending money in areas outside of music and audio equipment.