ZD,
Who said there is no reason? Who said the reason has to be explained to everyone (and it’s only an assumption that a reason wasn’t given). Parents should not give a reason for every rule they make for their children.
The principal did not say that the girl’s cannot wear high tops, she only said they can’t wear to school. (Read OP comment). So I am not sure what you mean about doing something different behind her back.
You differentiation between girls in charedi schools vs mo is inot factual in the least. One would wonder whether you have met girls who went to any schools.
Your comment is demeaning to girls in all schools.