Silke asks, "should it be OK for societies to frown on too much covering up the same way and with the same justification that they frown on too much uncovering." I think we could discuss general issues pertaining to societies, like France, that have legislated head-covering laws in recent years. First, I'd like to cover the subject of coercive communal "dress codes" with an emphasis on the Jewish community, as I see it.
I think the test of whether dress is prohibitively restrictive is whether individuals feel free to remove it, even if they choose not to do so. Certainly I'm not talking about being physically threatened, but purely about oppressive social pressure. Will they still be considered a member of the observant Jewish community? In America they are very much free to do so. In other words, if they did it, people would sigh and talk to their parents, but if they just refused, well, the rest would get on with their lives and, at most, try to make sure their sons or daughters were spending their time with someone else. There is an understanding that, in this society, you can't force people to do things; in fact, that only encourages deeper rebellion. You have to let people develop and try to guide them to the extent they let you. We don't excommunicate anyone (and we hope not to be excommunicated for our misdeeds in turn!). The fact is, there are perfectly good, sensible, and even deeply spiritual reasons why observant Jews wear modest dress. Forcing these laws and customs on people is the single most devastating way to ensure that they never get to internalize and appreciate what they're being coerced to do - you're robbing them of the choice to have a very meaningful experience.
It's a different situation and culture in Israel; less sweet carrot and more stick. There is a young woman I know who has not been married but has a young girl that goes to a religious Jewish school. They only became observant in the last few years. For months she would drop her daughter off at school, and the kids would ask her daughter where her father is. Because, if the mother is not wearing a wig or hat, it means she never got married, despite having the little girl. It's awkward socially. Anyway, it came to the point that the principle of the school mentioned it, so the young woman ended up wearing a wig to make things easier for her daughter. She says she likes it now, but I was furious when I heard this story. It's something that would never happen in America. If I heard Jewish kids talking that way about grown-ups I would smack them. The principle of the school had no business talking to her about it; she opted for the easy conversation with the mom rather than the more difficult and nuanced conversation with the kids who were speaking improperly.
It's just a situation that would not happen in the US, but in Israel, there's more pressure to conform, and there's no place to escape. If the young woman wanted to be part of the observant community she had to either put up with it or leave. It's such a small country; everyone knows you. If can't even go to another city, because everyone has cousins and uncles and people will recognize you. You have to be consistent, as the Russian expression goes, "blood through the nose", no matter what. Consistency is important in the US also, but to a much lesser extent. If I really wanted to, I could avoid contact with the Jewish community here, but in Israel, it would be impossible. Any inconsistency in your appearance or behavior would be observed and cataloged for future notice by the gossip army.
At the end of the day, the young woman wanted kids to stop talking negatively about her daughter and ended up wearing a wig. She's never been married, she didn't have to do it, but it was easier to conform than not, so she did. Now people know her like this, and it's become a part of her identity, so there's no point going backwards, but it's not the kind of thing I enjoy hearing about. It's not the kind of thing people should be taking on, voluntarily, I might add, solely because of public pressure, in my opinion.