So I’d argue that there is a dialectic relationship between the speech sensitivity on the left and the post-truth-I-know-it-is-false-but-I-will-say-it-anyways-tactics of the right.
And that isn’t the case because speech is a thing the left wants to take away from the rest of us ― no, speech itself has become the battlefield on which the decisions about the future are carried out. Both the left and the right have understood this. So I said the left and the right are in a dialectic relationship when it comes to speech. Here is what this means: As the discourse is getting more and more unhinged and boundaries we traditionally had are completely gone: things that were unspeakable a decade ago are now said in the news.
So the left is in their own weird way trying to keep control about what should and shouldn’t be said. The right on the other hand tries to expand what can be said, because it gives them an advantage. They literally don’t care about the fallout their language has on society as long as it brings them political power. The raw discourse certainly helps to divide the public into binary camps and the hope on the right is that the speech-aware left can be beaten by a right that is not bound to any ethical consideration when it comes to their choice of words. In fact the reason why the language on the right is so unhinged is because they belive it gives them a tactical advantage and not because any of them believes in free speech per se.
So the left tries to change speech in such a way, that the speaker should become aware of the many realities (race, class, gender, culture, ...) encoded in speech and avoid saying things that negatively impact others. The right literally tries to speak things into existence in a way that acts as a tribal identity in times where tribes cannot exist without friction. So where the left has accepted this post-tribal state of affairs and wants to respect as many realities as possible (and sometimes more) the right does the polar opposite and needs to keep as many realities as possible (and sometimes more) out of their speech in order to maintain the group.
That beeing said they are both phenomena that are rooted in the structural changes our societies are going through as a consequence of the internet and the fall of the soviet union (which meant for the first time capitalism didn’t had a socialist counterpart and there was no need to look social anymore).