The situation in Denmark is that we have a law forbidding people to wear masks, ski-masks or the like in public to minimise the risk of armed robberies or acts of terrorism. We have also had to demand that girls did not sit public exams wearing burkas with a face veil or the like, unless they were willing to unveil in the presence of a female member of the school or college staff. This came about because girls were identifying themselves by means of their national health card and in some, admittedly few cases, the card belonged to the girl who had enrolled for the exam, but the girl actually sitting the exam was not her, but her cousin or sister.
A much publicised case was the refusal of a bus driver to transport a woman who refused to unveil - he quoted the anti-terrorist laws and the courts found his contention valid.
After all as far back as the Partition riots, men in burkas were fairly common, as they more recently have been throwing bombs in Afghanistan, Pakistan or Israel.
In principle I agree people should be allowed to dress as they please. However, we have always had laws about public decency and public safety and some forms of clothing can be said to contravene these.
Most religions adapt to the society they are practised in - here most Muslims dress like everyone else, and have had, as has the Jewish community, to accept that the law in Denmark insists that bodies must be buried in coffins and not just in shrouds as both Jewish and Muslim religious ruling fine quite acceptable.