I'm going to make fun of my friends music taste
Why do you want to make fun of your friend's music taste?
She is such a nerd and thinks that everything she does is good.
It sounds like you're struggling with being a friend. You criticize her taste by telling her that you're opinion is right is a double standard. Support your friend and don't call her names or be rude towards her.
Nah, I don't care about her opinions or feelings.
Then I don't think you ever considered her a friend. It would be better if you just ended the relationship and found other people to hang out. People with similar tastes to your own will make you more comfortable.