> People ... will remove a mask if asked
Only if asked by somebody who has a right to ask! For example if you had a facial disfigurement, perhaps from a recent injury, you might feel more comfortable going out in a "mask" or some other item of concealing clothing and most indignant or hurt if any old Tom, Dick or Harry asked you to remove it for no "good" reason.
My own position on the burka is that I think it's s a bit odd but if women want to wear one then they have a right to. To provide a bit of context, I saw a debate on Newsnight(?) with several women in burkas, and it was like a scene from Monty Python. You couldn't tell who was speaking unless the camera was on them alone, and they kept interrupting each other because they couldn't read each other's body language! It was amusing. However, when they did manage to speak the women were all articulate and clearly wearing a burka out of choice, and all were quite comfortable with other women who chose not to wear a burka. Banning them from exercising their free will over a simple item of clothing seems draconian.