Solidarity, sacrifice and abdication.
The difference between formal and informal protest.
A protest might be organized and peaceful if it is centrally organized and seeks a small change in a policy. Such a protest seeks to work within the existing institutions for reform. Politicians speaking out right now almost all are asking for reforms within the existing structure. (As far as I can tell, I'd like to hear of counter examples.)
An informal protest need not be organized. Each individual participates based upon a shared sentiment. Quite often that involves a rejection of an institution responsible for an abuse. The protest is not able to negotiate or compromise (exchange) toward a mutually beneficial outcome. Instead, the institution is no longer considered legitimate. So, if the police loses its legitimacy and is rejected, people no longer obey the police, nor do people respect the things the police are supposed to accomplish. Police are supposed to protect property, so if people reject the police they will also violate property rights. They will violate traffic rules. They will violate terms of permits for peaceful protest. They do these things to demonstrate the rejection of the police, no so much considering the effects on other people.
A protest that gets a permit is affirming the legitimacy of the institution that issues the permit. That is to be expected for a protest over a policy issue within the existing structure, but not to be expected for a protest that has rejected the institution's legitimacy.
Similarly, advocating for people to exercise voice exclusively through voting also implicitly pushes people toward re-affirming of the existing institutions.
Police asking people for forgiveness or marching with protestors is a beautiful thing, but not consistent with the aims of the set of protestors seeking a constitutional change regarding the institution. Rather, those actions by the police attempt to retain the institution and to shift the protest back toward a policy change.
Un-centralized vs centralized protest.
We have observed both varieties of protest in the last few days, overlapping. Often the un-centralized protest will participate with the centralized protest, but then push it further.
This understandably threatens the peaceful protest, because it demonstrates that the leadership for the centrally organized protest cannot control the un-centralized protestors, and so cannot negotiate on their behalf. This makes it more difficult for the peaceful protesters to accomplish their policy goals.
Some people will participate for expressive aims rather than instrumental aims. Some people will participate in destruction of poverty because it is just fun. Some will march in a peaceful protest to signal something about themselves to others. Some will do it simply to impress a romantic interest.
Some will participate for purely self-interested reasons, such as looting. They have no intention of supporting the protest, though their actions indirectly support the un-centralized protest and weaken the centralized protest.
We also know that institutions can be very good for the welfare of the least of these and the flourishing of the city.
How should a peace lover respond to an institution that becomes abusive?
One appropriate response is to seek out ways to subvert the institution that has stepped outside its legitimate bounds. For example, blocking the path of the police, or overwhelming them by getting arrested. Using up the resources they would use in other ways. Perhaps we can show up without identification. Make it more difficult. Park illegally on the interstate with no registration.
Perhaps someone could have lain down next to George Floyd when he was being kneeled on, and demanded that the officer put his other knee on their neck.