There has been a lot of controversy in Europe about Muslim women wearing the versions of the veil that cover up nearly all the face but the eyes. Some of the objections many Westerners have are based on perfectly legitimate feminist and anti religious critiques of the practice. Some objections are based on disturbing hostility against Muslims as a class of people. Some European fears are based on centuries past Muslim conquests of much of that continent and the way that Muslim rulers mistreated Christians.
However, there is a very basic area of discomfort that doesn't get much discussed, at least in media readily available to Americans. I read this 3/31/10 Guardian article on the efforts in Belgium to ban that kind of veiling which actually touched on this (bolding mine).
Daniel Bacquelaine, the liberal MP who proposed the bill, said: "We cannot allow someone to claim the right to look at others without being seen.
"It is necessary that the law forbids the wearing of clothes that totally mask and enclose an individual. Wearing the burqa in public is not compatible with an open, liberal, tolerant society."
In Western culture, wearing masks has generally served three purposes:
1) A naughty attempt to get outside of oneself while in costume. (In the US, that nearly always means Halloween.)
2) A way to avoid being identified during criminal activity, usually violent.
3) A way to keep warm during really, really cold weather, usually when skiing.
The visceral reaction that one gets to seeing someone whose face is covered up outside of a masquerade party generally is one of alertness and danger. Seeing someone do this on a normal city street during summer automatically sets off alarm bells. Some non Muslims have taken advantage of the burqa to commit robberies in Europe, which speaks volumes on how the Western mind interprets the covered face. This follows in the more common practice of criminals using ski masks when they rob.
The problem isn't limited to this sense of alarms. We communicate very heavily using facial expressions. That is a big part of how we establish trust. Until confronted with such a cultural practice, we don't even think about how much face to face communication means to us.
Westerners have often been criticized with good reason for being culturally insensitive when they travel to other countries and even when they move there (e.g., "ugly Americans"). We aren't used to having people from other countries coming to us and setting off our cultural sensitivities.
Obviously, this isn't the only reason why the facial covering by some Muslim women bothers Westerners. But, it is an important part that seldom even gets discussed.