Every time someone says the word "peaceful protestor" I feel like they're missing a major point. Protestors are nonviolent, and nonviolent protestors are obviously better than the other kind, and police should act to prevent violence, but there's an
unstated major premise that the only valid reason for police action is to prevent violence. There are obviously lots of actions that police take against peaceful speeders, peaceful jaywalkers, peaceful loud-party-havers, and the peaceful publicly drunk and disorderly.
It's especially ironic to see "peaceful protestors" protesting against peaceful traders peacefully exchanging credit default swaps, or peaceful lenders peacefully issuing peaceful subprime mortgages at peacefully usurious rates, or peaceful lobbyists peacefully buying political influence with peaceful campaign donations, or the peaceful 1% peacefully lighting peaceful Cuban cigars with peaceful $100 bills aboard their peaceful yacht. Adding "peaceful" is missing the point and has nothing to do with whether non-peaceful law enforcers should or shouldn't do something about it.