Let's See Your Face at CNN.com
In the article, a muslim woman in small claims court refused to remove her naqib, which is the head covering some muslim women wear that only allows the eyes to be seen. The judge told her, "I need to see your entire face so I can judge for myself whether you're telling the truth or lying." Because the woman refused to do so, the judge dismissed her case.
I think I agree, somewhat reluctantly, with the judge. Modern society runs into several issues with head coverings of this nature. If a muslim woman is going to refuse to let herself be seen or identified, then she probably needs to remain hidden permanently behind a man. If she's going to act as an independent person, doing things such as renting and driving cars, then she needs to assume that at some point she is going to need to clearly identify herself as herself.
And this means the person who is asking to see who she is needs to SEE WHO SHE IS. That is, remove the headgear.
It is unreasonable to assume that privacy for such an incident is going to be available. It is equally unreasonable to assume only women will ask for that proof. The rest of society can not be expected to make special consideration for her beliefs. That can only go so far.
If she were there strictly to add supporting information to a case, perhaps there's some leeway. But as this specific case hinged entirely on her testimony, it is unfair to expect to be able to hide from the judge and from the legal opponent.
I respect her right to belief what she wants. But in this case, she wanted other people to be bound by her beliefs. And that's not fair to them.