I would not participate in either (and I think I would not participate in the American Revolution if it were to happen today). But different motivations will respond differently to similar responses.
A few thoughts:
Revolutionary protest (protest that seeks to destroy an existing institution) reduces the cost of criminal behavior. That is not accidental. The criminals may not really be interested in forwarding the revolutionaries' agenda, but their actions do have that consequence.
Reformative protest (protest that seeks to reform an existing institution) is in tension with revolutionary protest. However, reformative protest reduces the cost of revolutionary protest.
We observe reformative protesters cooperating with and helping the police to constrain revolutionary protesters and criminals. This demonstrates that reformative protest does not seek to destroy the existing institution. So the reformative protest makes it easier for revolutionary protesters to move, but reformative protesters try to constrain the revolutionary protesters.
The reformative protest might become the legitimate institution, or the legitimising institution, the institution that generates legitimacy for other institutions.
The reformative protest could respond to new police action that steps beyond what seems appropriate, and the reformative protest could spawn more revolutionaries.
Similarly the revolutionaries could go too far, and some participants could revert to reform.
Put another way..
The difference between reformers and revolutionaries is that the reformer has more at stake in the current institutional framework than the revolutionary. Revolutionary change furthermore involves a non-marginal cost that may overwhelm the benefit of reform. Economists, by nature and by training, prefer marginal changes.
In the current context, the agitators are promoting views that go beyond the current protest. A white-supremist obviously has no concern about police violence, but sees rioting as an opportunity to provoke a crack down. A black-nationalist or anarchist may likewise see rioting as a way to force moderates to pick a side, presumably theirs. Right or left, the current protests represent largely un-channelled anger and an opportunity to channel that anger in new directions.
The stories that get told right now will determine which way this protest will be channelled. Unfortunately, moderates do not have an effective voice in the current environment.