I know of at least three possible minds for this. Pretty sure we all assumed we were typical until talking about it.

• One friend of mine is like you, and finds music horribly distracting to reading.
• Another friend becomes practically deaf while reading, so music is just irrelevant.
• I, on the third hand, can sing along to songs I know, while reading. I can possibly even do this for simple songs I don't know. I would suspect this is not optimal reading from a comprehension or speed perspective, but it's a lot of fun.