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.
Seems like you were spot on, if the translation of Chapter 4's first page ("So you went back to black hair") is accurate.
Japan is not really exceptionally conformist, it's just easier to see there because conformity is part of the culture. For example, as much as Americans love going on about how their country is the land of the free, their society is just as conformist at the core, they just don't like thinking about it because they like feeling special.
There's a world of difference between societies that have had to adjust to diversity - however reluctantly and irrespective of how many refuseniks are still tilting at windmills over it - and ones that, well, have not.
Case in point pretty sure that the kind of crude appearance policing on display here would be more likely than not to get the school sued very quickly in the notoriously prickly and litigation-happy US of A.
Yeah, I admit I made the mistake of forgetting to mention another big factor that is at work: The cultures of East Asia are predominantly "collectivist" (i.e. the group comes before the individual), where as Europe and the Americas are generally pretty big on individualism, even when a given culture has a significant degree of conformist bent. Basically, in a country like the USA, there's a tightrope balance between individualism and conformism, while in Japan the high conformism is exacerbated even further by a collectivist mentality, hence the unusual extremes of its manifestations in comparison.