I get where you're coming from. Correct me if I'm misunderstanding but you feel one side is shutting down conversations and any attempt to change the narrative gets painted as adversarial. This is bullshit virtue signaling. And it seems the only way to garner engagement is with ever increasing extremism.
When I say consequence, I mean it in a non judgemental way. Garnering a consequence does not mean they are in the right and you are in the wrong.
I don't have an answer how to solve this. If I did, the world would be all peace and love. But it aint. I think there is an element of two wrongs don't make a right. Increasing extremism gets engagement but at some point its a net negative on society. Similarly, a level of self control and self sensorship can help people in a sociery get along. But censorship and shutting down conversation/discourse quickly becomes net negative also since it just builds resentment and anger.
In the end, too many people are babies and can't mentally handle opposing thought or level headed discussion. This is on all sides imo.