In my country a Nazi or a Communist site would simply be shut down with a court order, because that sort of thing is illegal here.

See - it actually works. There's no Nazi party here. Nobody is marching with Nazi flags. And nobody is hosting Nazi sites.

So pass a law that criminalises Nazism like most European countries have done.

I prefer clear rules of what speech is forbidden and not having extra-judicial punishments for speech that is legal.