What is music children shouldn't hear? Sad? Frustrated? Filled with complicated emotions? Are you saying children shouldn't learn to feel complicated emotions so they can be emotionally stunted!?!
makes no sense
It's hard to communicate the implication. She doesn't actually say delinquent, she says "poor taste" or "bad character."
Typically, dyed hair and piercings are classic playboy characteristics. These types are thought of as fake, uncaring people in Japanese culture. I think she's implying that if the music is "half-assed" or "fake," she's going to cut her off. It's like the guy who says he loves guitar but only knows Wonderwall (a notorious beginner song).
The Japanese itself is pretty open-ended, so it's difficult to translate in a clear way while still being true to the source.
If it's genuinely confusing people, I might modify the translation or add a note. Please let me know.
Edit: Note added