Yeah, Japan is obsessed with its ethnic homogeniety and societal conformity to frankly unhealthy degrees. Why do you think the country is facing an ageing population crisis? The government and the general populace are heavily opposed to the concept of "tainting" the practically pure Japanese makeup of their population with immigrants from "barbaric" countries; they could barely tolerate the Chinese, Koreans and other East Asians that they do allow in small numbers as it is.
Read about the rampant racism against American and European expatriates to Japan sometime. It's astonishing.
I suppose it wasn't her real hair colour? If she was telling the truth and they insisted it be dyed just so she fit in, they could all go die in fire for all I'd care. She shouldn't need to blend in and pretend - but Like I said she was probably lying.
It's a common theme though. First that comes to mind is redheaded Youko in Juuni Kokuki, but there's plenty of other characters that get that "dye your hair to blend in" treatment.
There's also Ichigo Kurosaki and Orihime Inoue from Bleach; neither of them dye their naturally orange/reddish-colored hair, but both suffer from that decision, as the former has a false reputation of being a violent delinquent (he's violence-prone, yes, but only against bullies and other unsavory sorts that do deserve violence), and the latter nearly had her long hair cut extremely short as a little girl by some female bullies if it weren't for the black-haired future-blackbelt Tatsuki Arisawa violently defending her in outrage, starting their lifelong friendship and making Orihime treasure her hair rather than hate it like she used to.