Context: https://en.wikipedia.org/wiki/Self-censorship
Self-censorship is the act of censoring or classifying one’s own discourse, typically out of fear or deference to the perceived preferences, sensibilities, or infallibility of others, and often without overt external pressure.
Very often. I regularly consciously do not post comments, or write something and then don’t post it.
I think you could call it self-regulation, though. It’s better we don’t always share everything in every situation.