Talking as a veteran of a bunch of anti-fascist actions, I can say that the only difference in policing I've ever seen when it comes to the far-right is that the police pretty much do what they can to avoid confrontation. Their standard operating procedure is to stand back and form a cordon to separate them from counter-protesters, but they go out of their way to not actively confront them unless they absolutely have to.
Whereas anti-fascists are treated much more harshly - from the passive (look which side the facial recognition cameras are focused on, for example) to the active (which way the riot police stand with batons drawn, and who they use them on preemptively), British cops really do not treat us the same. This also applies to left-wing groups more widely, going back decades. Infiltration by undercover cops, covert surveillance, and dawn raids to drag people into stations ahead of actions. Often these arrests are later judged unlawful by the courts and the police have to pay out compensation (this happened to some friends just a few months ago for a mass kettling and arrest of a peaceful march back in 2012, and I know plenty of people who have been on the periphery of some of the things coming up in the spy cops enquiry), but it's a price they see worth paying because, in the longer term, it means they can seize electronic devices for intelligence, and they can build up data on who's involved in what. (Side note, but this is partly why XR and JSO have have had a lot of success recently, for what it's worth - their memberships tend to be older, often retirees living in small villages and towns with no prior connections to the more longstanding environmental protest movement, so there isn't a lot of this intelligence in place on their networks that the police can use to anticipate actions... Whereas the crusties of the post-New Age Traveller movement, moree active from the 80s-00s, have largely been put in their place.)
In the context of what we're seeing over the last week, I think it's pretty clear that the standard police tactics with the far-right aren't working because these pogroms are just so widespread. And I think it's very easy for people who aren't living in a community targeted by the far-right to wash their hands and say it's just violence on both sides, people looking for a fight, whatever. Fascists instigate all this. They go looking to smash up neighbourhoods and high streets, they deliberately provoke and assault people, and in those circumstances people have every right to defend themselves, their neighbours, their friends, and their families. To sit back and do nothing is not a neutral, peaceful choice - it is a choice to let things get even worse.
And I'm not just speaking from personal experience here - this is the long history of how fascism gets pushed back, it has always relied on the larger mass of regular people standing up and saying "no more". We can condemn individual cases of violence within that organic response, but by the time counter-actions are being assembled it's too late, law and order has broken down and violence is coming. It's just a question of how much people are willing to accept before they respond.