Whether you like it or not, yarmulke styles do represent hashkafos.
Right now, I have a very large, completely black kippah serugah on my head. So, what hashkafah to I represent? Modern Chareidi?
It’s not even relevant why the child might “want” to wear a kippah serugah; if the school told him not to, he shouldn’t.
It may not be relevant, but it still obviously mattered. That’s *exactly* the kind of situation that calls for further discussion to get to the root of why it matters, rather than just a “do it because that’s the rule” type of answer.
The Wolf