Protests can (and admittedly often do) devolve into shouting matches, but not necessarily. As I've aged I've reached the understanding that those never accomplish anything positive or useful. As such, I rarely bother anymore - if I go to a protest, I'm there simply to be counted as one of the (hopefully) many on that side of things. I do my best not to allow myself to be baited because it's just so pointless.

Do I censor myself? Maybe - if you consider choosing not to bother arguing a point because it seems likely that they're not going to engage in good faith to be self-censoring. Otherwise, not really - I do try to consider my words carefully because there can be a LOT of logical steps to an argument that I don't normally consciously think about as I likely reached my stance a LONG time ago and all that immediately comes to mind is my final conclusion.

My life involved significant patches of effective solitude, and so I never really had to learn to argue my perspectives until I was old/mature enough to understand the importance of politics. Up until then, my thought processes were solely focused on determining the end result - the important things to remember. All the steps that got me to a final answer weren't important enough to bother trying to remember because I usually didn't need to recall them very often.

Unfortunately, politics is ALL about arguing those individual steps before the final conclusion I reached, but my brain wasn't trained during my lifetime to work that way - so I have to think out what I'm saying each time. It's why I prefer this text-based type of social site - I can't think on the spot quickly enough to do video, for example.

So if you consider that to be self-censorship, well I disagree. I consider it making sure I'm communicating what I intend to effectively so that the conversation doesn't get derailed too easily.