I'd protest about anything me... indeed I have ... in the past... I was moderately *famous* around these parts for my wildlife advocacy and as part of that I got co-opted onto a housing protest group, of which I became vice chair.. I'd protest - not that I believe it does much good, in terms of action, why not it's kinda our civil right... we don't have much that we can do when things seem unjust.
I participated in protests against Chancellor Katehi after the UC Davis pepper spray incident. But there was only one side to that protest and the best protest we did was a silent treatment "walk of shame" for her after she left a meeting.
I would probably steer clear of any protests where there are two clashing sides. Not worth it if it means I'm going to get run over or stabbed.