The face veil (niqab) is actually quite controversial even here in the Arab world.  I know a lot of people, even conservative Muslims, who think it gets taken way too far.  In most places that I've been where it's worn, women are prepared to remove it for identification purposes.

But the headscarf, honestly, I don't get why it's an issue.  I'm not a Muslim, but sometimes when I'm having a particularly bad hair day, I will hide my hair under a funky scarf.  Would I not be allowed to do that if I were a teacher in Bavaria?  Or is it only Muslim women who wouldn't be allowed to cover their heads?