I think we are both more responsible for the actions of our own side than we are for the other’s. Blind partisans who rely on brute tactics (psychological or physical) only ever view an appeal from the opposite side as an attack, and will ‘attack back’ in turn, making everything worse.
levelheaded people can modulate their opinion when appealed to, but these people are usually in the minority of an ideological debate (obviously) and the individual understanding of a level-headed few won’t change the current mess. That is where internal change starts.
We are, of course, not ‘responsible’ for other people’s actions in that we should not feel guilty for them, but also that attitude leaves unchanged the state of “partisans + chaos”.
Hypothetically: If the level-headed few convince their side’s outraged, misguided majority, it will slowly force the extremists back to the fringe through peer pressure.
Even if there’s no moral compulsion to calm down our sides of the mob, we should at least feel obliged to in pursuit of our ideals.
If the mobs never calm down then intelligence is drowned out and you might as well give up on achieving anything constructive ever.