One possible reaction to a moral panic is another moral panic and that's exactly where I think we are here.
Cancel-culture panic is a largely anecdote and feelings-driven. There's no real data to show that firings or social consequences for speech are more numerous or more severe or more unjust (or even more "left-wing") today than they have been at any point in the past.
And in many of these anecdotes that seem to drive the discourse, nothing of note actually happens to the person who was "cancelled" - they are the subject of an investigation or social media dust-up for a news cycle. Then life carries on.