"It's kind of illegal to force someone to take off their clothes when going into a building.."
Really?
I've visited a number of buildings in central London (including the Royal Albert Hall) where I have been asked to remove my overcoat and on one occasion my jacket. More than that, try getting through security at any airport without removing your hat, coat, scarf, jacket, gloves, very often your shoes and occasionally even more than that. I accept that at that point you are not technically "entering a building" but simply moving to a different part of the one you're already in but the principle applies.
I hope you don't consider I'm too thick by pointing this out. There's nothing illegal or unreasonable to expect people to show their faces when entering any public establishment or for that matter a private one. (I wouldn't allow anybody into my house when masked up). The sooner Muslim women understand that people in this country do not routinely go about masked up the better. Nobody can prevent the stupidity of some women to accede to the wearing of this ridiculous garment but no special provisions should be made for them to do so.