I do think the police should act to try and prevent violent groups from committing violence. Your position seems to be that the state should accept violence as long as the people committing it claim to be political? If anything organised political violence is the type of violence that it's the most important to prevent because it has by far the largest potential for harm.
I can talk about specific things the UK police have done when targeting 'extremist' groups and how I disprove of them if you want (undercover police assuming fake identities to the extent of having children with women in the targeted groups being one). But disapproving of specific things isn't the same as saying the police shouldn't be investigating and infiltrating organisations advocating violent ideologies.
It is dangerous to believe "oh, I don't care what an oppressive government does in order to stop Nazis" because a whole lot of people are being called Nazis these days.
The same exact thing happened during the red scare. It was not JUST the revolutionary communists who were literally trying to overthrow the government that got oppressed. A whole lot of other people who definitely didn't deserve it, got oppressed to.
Human rights exist for everyone for a reason.
So what you are saying is, that all the police have to do is label someone a Nazi, and you'll give them a free pass for whatever it is that they do?