I know the feeling, in my eyes excessive display of religious affiliation in clothing tends to come over as a certain kind of smugness: "according to my values, i am infinitely superior to you godless crowd". Hardly the most respectful message to send, a bit like the difference between a vegan and a preaching vegan.

Still, if you'd want to put up legal barriers to displays of religion, you'd certainly need to find better reasons than "it makes people seem very arrogant" ;)

Schools, being places of science, might mandate non-religious clothing in the same way monasteries and temples should be free to set clothing regulation inside their premises.