It seems harmless enough on its own, but looking back on my own life, my impulses to get pierced and dye my hair and wear funny clothes were basically a cry for help, low self esteem, rebelliousness and dissatisfaction with life. My parents were very supportive of the kinds of things I wanted to do, to a point anyway. I grew my hair all in front of my face and spent an hour doing it every morning before school. I got in so much trouble from school for the way my hair was, and yet my parents supported me. Frankly they should have yielded to the authority of the school in this matter. I was out of control. In the years to come I would lose my faith entirely, get two girls pregnant in a row, cohabitate with even more, plow through job after job, and ultimately become homeless and destitute, all the while plagued by atheism and bipolar disorder.
Dyed hair in itself is not a problem, but I would regard it as a harbinger of things to come. I think children should learn the values of conformity and obedience and proper appearance, modesty and hygiene, and letting them do whatever with their hair may not be the way to go. You will not win any wars by preventing them from doing something like this, but Rome was not built in a day. On the other hand, if you trust your child, and you think that this will teach them a valuable lesson in that they will find out how people react and regard them as freaks, go for it and let them do it. Kind of like letting your kid get hurt so they know how it feels the next time.