Is it normal that I do not enjoy listening to music?

You bring up an excellent point.
People listen to music because it's an form of entertainment, and it moves people emotionally because [the listeners] believe it relates to them.
Different genre's are meant to have different moods and actions.
Hip-hop/Rap makes people heartless, and this is why you see crimes of robbing and shooting.
Rock makes people change their minds, but it all depends on different songs. (Some songs convert religion into worshipping the devil)
If you don't like music... Superb.
Don't let any form of entertainment change you.

I listen to music.. But I block all the negative influence. But this isn't about me..
It's about you.