I edited your post, maybe you now see why your whole line of reasoning doesn't make any sense whatsoever?
A Nazi uniform is a uniform associated with the attempt to systematically destroy the Jewish people. The perpetrators of that heinous crime where overwhelmingly white Europeans. Nowadays, Nazi uniforms are most often worn by white Europeans or their descendants. Them wearing it can almost always be interpreted as them wanting to associate themselves with Nazis. Often they proudly declare their allegiance to Nazism.
A face veil is a cultural and religious article of clothing associated with rules on modesty within certain minority interpretations of islam. These interpretations can be held by both men and women. The face veil is often attacked from many sides. Many islamic theologians claim that it is not actually islamic. Many orientalists claim that it is a clear sign of islam's backwardness and inferiority in comparison to the west. Many feminist claim it is a misogynist method of patriarchy to control and dehumanize women. While I agree with the first and last of those arguments I can still see a difference between Nazi uniforms and face veils.
If you cannot see the differences between Nazi uniforms and face veils, however, I just want to point out that Nazi uniforms aren't banned in most place and that I personally would never support a ban on Nazi uniforms. So your comparison is moot either way.
No, not a single one in the whole world. If a woman "wants" to wear it, then only because she was brainwashed.
I'm all for religious freedom (I would go protesting on the street right now if I would live in America, don't get me wrong here). But I think this is really harmful for a modern society.
Anybody that does away with women's choices out of hand, without even listening to them, because they just assume the women must be brain-washed is no progressive or feminist in my eyes. Feel free to go through my post history if you're curious to what some women wearing a face veil have said about their reasons for doing so. Their intelligence, assertiveness and just general "being a capable and adult human being"-ness might surprise you.
Also some of you seem incapable of seeing the difference between being an advocate of listening to the women affected by a ban, respecting them as human being (i.e. not calling them stupid or brainwashed) and supporting their freedom to wear what they want with being a denier of the misogyny behind a face veil or an advocate of wearing one. I am the former, not the latter.