I agree. But I also know that all people do not parent the same way.
Why does your child want to dye her hair? Maybe if you find that out then you can quickly get her mind off of it. For instance, if it's a certain movie character with pink hair then stop allowing her to watch that character and I'm sure she will forget about it.
If it were me, I'd likely do a gel in her hair during the summer months and wash it out at the end of the day. I'd also let her know she can't go out of the house in public with it in her hair. This is what I do to teach my kids rules and what is right and wrong in my eyes. I don't agree with it at all but it can't really hurt anything for one day.
I know though, to each his own.