We shouldn't do anything now but if it gets out of control then yes of course but if it's harmless then they can believe what they want to believe everyone has a right to.
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Think of the last movement of Nazis. It was bad and millions of people died. These "new" Nazis could and may turn into the same thing causing millions more of deaths that aren't just Jews but gays, lesbians, and other minorities that they have an issue about. People should start protesting anti-Nazism to counter their arguments when they protest pro-Nazism.
Yes we should do something and that something is to educate ourselves and maybe even educate them. Not that we should try and stop them from doing something that isn't illegal and protected by free speech. As long as they don't commit a crime why should we tell them they have to accept everyone. We can try and teach them that we are not that different and that skin color is truly only a reaction to the amount of sun exposure our ancestors and us have had. Ignorance needs to be eliminated. Education is the key and from that stand point we should do something about the Neo-Nazi movements. Again EDUCATE them and ourselves.
I wasn't aware of renewal of Neo-Nazism although there tends to be a rise in anti-semitism when times are financially tight. If there is a new movement, I think we should do what we can to educate people about the groups but they do have a right to exist--at least in the US. Germany has strict anti-holocaust denial laws so I cannot go into what they should do. As a country with freedom of expression, there isn't much to be done except if the actions fall under the banner of hate crimes.
Everyone has their right to free speech. If they want to use their freedom to be hateful, then that is their own prerogative. They will of course, suffer the consequences of being outcasts to the rest of society and will probably be less privileged on account of that. If you are going to "do something" about Neo-Nazis, that opens up the possibilities of discriminating against other groups at the government level, which of course, would also be bad.
If anything should be done about Neo-Nazi movements, it should be the fostering of a society that educates people about other cultures, especially with children. Typically if you are a Neo-Nazi it's because you were exposed to racism when you were younger and built that identity before you really experienced the world around you.
The true modern brown-shirts, those who seek out those they disagree with and violently attack them, are mostly the anti-racist/anti-fascist groups. I can't remember the last time I heard of a significant attack by "Nazi" group in the USA, but the Anti-Fascist/Anti-Racist are assaulting people in Europe and the USA all the time, sometimes just for opposing illegal immigration or expressing pride in their own European (white) heritage.
Just one example: In 2012 Chicago, a group of 18 people dressed in black, wearing masks, wielding steel batons and hammers and claiming to be extreme anti-racists stormed a suburban Chicago family restaurant in broad daylight to assault a meeting of a "European Heritage Association" group who were dining there. As they stormed the restaurant, anyone who stood up was struck with weapons. Ten people were injured and three people required medical treatment for head wounds, including a 70+ year old man.
This is what leftist mean when they say "do something" about so-called Neo-Nazi groups. They support groups who take "direct action", meaning violently attack those they disagree with. The irony is that they have become they very kind of people they claim to be against, just with a different political spin. So I say "No".
Those people in democratic nations are supposed to be allowed to believe what they want to -- this includes having Neo-Nazi opinions. While past No-Nazi actions were harmful to many people, we can not prejudge people based on our fears. As free citizens, the members of this movement should not be acted against prematurely. Like all citizens, they should only be acted against for crimes they commit or plan to commit.