You owe your parents an extra measure of respect. Listen to their opinions, rather than treating them as the opinions of a stranger. If their minds start to fail, do not point it out when it is not necessary. Be very gentle when it is necessary.
If coloring your hair is important to you, then you go ahead. I would not give reasons, because this is an invitation to an argument. I would say, “I know you don’t like it, Dad and Mom, but I hope you’ll look past it. You’ve made your point, but I’ve decided to try to see if I’ll like it, anyway. You are my parents, so I gave you room to throw in your opinion. I’m a grown-up, though. It is my hair color–this much, I get to decide.”
If you think about it and it just isn’t that important, then don’t color it. Choosing one of several possibilities that you could like partly because it would please your parents isn’t a bad thing. Just do youself a favor and give yourself credit. Don’t resent them, because in the end it is your decision. Instead, enjoy what you did with your hair instead as: “I like this, too, plus it pleased the parents. And maybe they’re right about Reason X, who knows. But this makes both of us happy.”