I would never stop reading a story just because a characters hair is dyed. I feel like it’s an interesting choice on the authors part. As for backstory, I don’t think you need to give a reason on why the characters hair is dyed. If you think about it, most of the people in real life don’t have a reason, other than that they think it represents their personality / looks cool / everyone else is doing it.
So, I don’t think you have a problem at all. It would give your character a cool personality trait, and somewhat differentiate that character from others.