Well, censorship has been recentky applied to Palestine Action supporters too (they're routinely arrested in the UK, and they're normally far leftists), so it's not only nazis. The thing that makes hate speech laws safe and fuzzy is that they're initially applied to restrict the speech of your enemies. Then the tide changes, and the same laws get applied against you and your friends.
They're not excusing themselves with "I can say whatever I want to" and "arrests for speech are invalid", are they? - they're not hiding behind free speech. They're excusing themselves with reasons like "You're arresting me for terrorism but I didn't do any terrorism" and "The UK is helping Israel do the next Holocaust, and it's important that we talk about that and hopefully stop doing it"
