As others have said, it's just hair. This is probably the most harmless creative outlet (aside from wacky clothing) that they could want. I'd much rather have my child dying their hair wild colors, than begging for consent for piercings or tattoos, which would be more difficult to correct if they changed their mind later. :P
Starting from around age 14, my hair was a rainbow of colors. I'll never forget my father coming home to tell me about his new highschool co-op student, who went in that morning to say "Oh my gosh, there's this girl who got on the bus this morning with half of her hair blue and half of her hair pink. What the hell was she thinking. She's insane!" to which my father responded "Uh yeah...that'd be my daughter."

Woops.
Being a natural blond at the time, my only advice would be to avoid dyes with "ash" in the name. They'll turn a blond's hair green. But I was very grateful that my parents were so cool with letting me dye my OWN hair. I got it all out of my system in my teens, and actually haven't had dye in my hair (even normal colors) in - wow - 10 years now. I plan to naturally grey.

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