generally, you want the police response to protesters to be as light as possible, especially during tense political situations, so suggestions that the police weren't heavy-handed enough are both illiberal and wrong-headed; those arguments will not help anybody except the bourgeois class. we've been over this with nazis in this society over and over and there's an established free speech position when it comes to them - the legal precedent is actually that you let them march, you just keep an eye on them, and you get ready to step in if you have to. this is rooted in the observation that there is a difference between a contingent of brownshirts and a contingent of drunk sports fans, and one poses a threat to society that the other one simply does not. using the wonders of modern technology, any property damage or other sorts of violence that are carried out by looters or rioters can be prosecuted after the fact.
so, that's actually what the right thing for law enforcement to do at the time is, and probably what they're trained to do: you let them sweep through, you just slow them down, and then you figure out who they were afterwards.
this may not be the way that the police behave when dealing with protests or other types of demonstrations that are organized and populated mostly by people of african-american descent, specifically. the reasons for this are equally simple - the police are trained to deal with black protesters as though they're representatives of a paramilitary group or a political opposition. and, in truth, these black protest organizations are far better organized and far more disciplined than any of these nazi groups are. your sympathies may lie where they lay, but the state is concerned about it's own self-interest first and foremost, and the black protest groups are far more dangerous to it than any ragtag clown posse of nazis are.
for that reason, the differences in response are in fact deeply rational, and quite tactical. it just requires understanding how the state sees you, and how you pertain to the various movements occurring in reality around you.
but, are these state assumptions free of racial basis, fundamentally fair and how we want to exist, as a culture? i think it's fairly clear that they are none of these things, and should be reanalyzed for what they are.
if there is to be a policy discussion and a change in direction, it ought to be to liberalize policing practices around black protests, not to crack down harder on the nazis. the last thing you want to do is martyr a bunch of fucking nazis. no, the problem here is not that the cops were too lenient in their treatment of the storming on capitol hill, but rather that they're unnecessarily aggressive in how they deal with what are primarily middle class reformists in the black protest movements, that would have little capacity to participate in an armed insurrection if one appeared in front of them.
you don't want the nazi protests to look like the blm protests; you want the blm protests to look like the nazi protests. and, that shouldn't be so convincing a thing to put into practice, nowadays.
the second thing is the issue of police violence on the demonstrators, and we should at least be questioning whether it was a justified use of force, as i don't suspect it was. why aren't the defund the police people upset that this woman got shot? i mean, they should be, shouldn't they? and, i'm curious to get some direct answers and responses, as it may help expose some contradictions and biases. i mean, is it because the cops are there to protect you, so killing her was ok? that would be a remarkable thing to hear from a defund the police protester. is it really all race-reductive arguments, to the point where murdering a white woman......doesn't matter? i mean, where's the consistency of thought, here? what's your (probably terrible.) argument?