When I first met someone I knew was gay, many years ago, I was very ill at ease. The first time I conversed with someone wearing a safety pin through her eyebrow, likewise. In both cases, I got over it. I suspect that if they had no choice, the anti-burqa crowd would adapt as well.
A more imaginative argument is that covering the face is an attack on civilized norms. "The niqab and the burqa represent a refusal to exist as a person in the eyes of others," says French parliamentary leader Jean-Francois Cope. Journalist Christopher Hitchens calls them "the most aggressive sign of a refusal to integrate or accommodate."
But in a free society, none of us is obligated to integrate. The Amish don't. Neither do the Hare Krishnas. Or Trappist monks. Wearing a suicide bomb around your waist is aggressive. Concealing your face is peaceable.
Veiled women are not refusing to exist in the eyes of others. They, like all the rest of us, are merely deciding on what terms to make their existence visible.
It's also claimed that covered faces are a security threat, since criminals have donned burqas in a handful of instances. Veils can be put to sinister uses -- just as scarves, ski masks and sunglasses are often worn by camera-shy bank robbers. We don't ban those, and absent compelling evidence of an epidemic of burqa-enabled felonies, we shouldn't ban veils.
Contrary to the prohibitionists, being deprived of an option is not liberation, and choosing your own clothing is not aggression. The few Muslims who take cover behind the burqa should be tolerated as long as they observe the first axiom of a free society: Live and let live. Maybe someday their opponents will learn to do the same.