The flag is analogous to the swastika in that they were both political symbols that people rallied to. They were both symbols of governments that systematically oppressed a particular group of people. (The Confederate flag is a symbol of oppression that is deeply offensive to some. It's called "slavery." Look it up. What it symbolizes to whom is far more complex than secession from the central governmnent. Do not make the mistake of underestimating the race related associations of said flag. Not everybody has that association, like not every group views the swastika as inherently bad. However, plenty of people do.) And those symbols are both deeply, deeply offensive to some groups of people. I am not trying to compare them in terms of "which government was worse," or "which group of people is more morally culpable" or "who was more oppressive" or even which has more shock value. Those are pointless arguments. It's about what happens when people display the symbols once the war is over and civil (rather than martial) law is established. I do not think the swastika should be illegal for an individual to display in Germany. I do not think the Confederate flag should be illegal for an individual to display in the South. I think it should be a matter for individual consciences.
There is a difference between limiting someone's ability to harm someone else or discriminate against someone else and limiting their ability to speak their mind or point of view. It should absolutely be illegal to assault someone, to hold someone as property, to refuse to accept someone's money based on gender, ethnicity, etc. It should NOT be illegal to express your opinion regarding those groups unless the act of doing so prevents them from exercising their rights to the same capacity (e.g., creating a hostile work environment so that a person's ability to do their job is compromised).
People can wear white sheets and burn crosses (on their own property and time) all they want. That is not (and should not be) illegal. What is (and ought to be) illegal is actually harrassing, harming, and oppressing other people. Preventing citizens from voting. Threats and blackmail.
It is not illegal to wear a burqa, and should not be. Ultimately, the woman is making a choice to put it on, to remain in the marriage, etc. If she is being threatened or harmed for making the choice, that threat or harm is the crime -- not the clothing. It shouldn't be any more illegal to wear a burqa than to wear a bikini. (And you could easily argue that wearing a bikini is a symbol of oppression as well, in that you could say it was designed with the purpose of objectifying women for the viewing pleasure of men.) What does need to be addressed is actually treating women like property, rape, assault, honor killings, genital mutilation, etc.
Censoring people's freedom of expression in personal choices isn't just a slippery slope. It's a steep grade hill that has just been greased and has banana peels scattered here and there. Wearing a burqa could be easily viewed as a form of censorship in and of itself. Beyond some pretty common sense rules (e.g., don't shout fire in a theater), it is not acceptable for any group of people to say, "I disagree with the way you limit other people's freedom of expression, so I am going to limit everyone's freedom of expression because I know what's right." You are replacing that person's form of parentalism with your own. And that is not an acceptable attitude to have towards other adults. The fact that people are wrong does not affect their rights. In general, autonomy trumps stupidity.
I understand that in the US people no longer have the freedom to discriminate in terms of race or gender for that same reason, because people couldn't be trusted with that freedom without hurting large segments of the population.
People as private individuals in the United States have every right to discriminate, actually. I can refuse to go to a church which allows women to serve as ministers. I can refuse to give my business to a store that is patronized by GLBT people. I can go to white supremacy websites and write long essays on how no other race deserves to interact with white people except as servants. I can do all sorts of things the majority of people would find morally abhorrent if I am acting as a private citizen. Because those things do not limit other people's rights in any way. They can speak back. They can refuse to listen. They can refuse to vote for me. A publisher can refuse to accept my essay in their journal. Whatever.
What I
cannot do is discriminate by refusing someone else the ability to exercise their own rights (to gainful employment, to purchase property, to attend school, to run for office) based on my personal beliefs.