IMO, Scarves are fine (on the street only). The problem is the Mosque's prayer call (for reasons of noise pollution, and the very same that Islam doesn't allow people of other religions to pray out loud, even in their own places of worship - see Dhimmi status), the total Hijab, a total Hijab should also be alright, only that it will threaten security and we won't be able to make use of security cams, and people won't be able to identify the person. Same as wearing any other mask in public.
The problem lies when say muslim hair-dressers, want to wear scarves, and they get fired, just as anyone else who wanted to wear a headscarf (while one of the critical requirements of the job is to show hair), then they sue. They have no right, religion should be solely personal, and you would be subject to the very same treatment as everybody else. Muslims should also not expect, from the public, to be treated any differently from a person in a pumpkin costume