I believe a better question to ask yourself in such a situation is "Are you ready to avoid senseless violence?" ie. "is this worth it?" I don't believe is worth fighting police during a demonstration. I'm biased, sure, but still if you are in such situation you need to stop for a moment and think about such questions.
Whenever I went to demonstrations -and, granted, its been a while since War in Iraq started- I made a very conscious decision about this beforehand. Its part of planning, because it might affect your OPSEC (things such as your possessions and your planned behavior).
I also believe its not a valid comparison between physical violence and emotional violence (such as threats). I'm currently reading Ronan Farrow's Catch and Kill, and I keep thinking: "now this is a fight worth fighting for". I'm at 2/3 and I have not read about physical violence [against the reporter, Farrow; not referring to the violated women!] as of yet.