Even private schools where I’m from are unlikely to have that kind of thing. They might have a uniform, but I’m not sure if dress codes are even allowed.
I suppose the exception would be if someone is wearing something that can be considered offensive. E.g. if they come to school in an SS uniform. That’d definitely cause a commotion. I’ve no idea how a hairstyle could be offensive unless someone shaved/shaped their hair into like a slur or something.