Indeed there are many media stories on ‘cancel culture’ - supporting my point that the aim is to impose culture war on the news agenda. Look more closely into the actual details behind those stories and you will generally find there’s little to them. Tweak the search a little - to, say, ‘cancel culture myth’, and you will find hundreds of repudiations of those same stories. Try it!
Incidentally, the ‘left opinions’ you offer are not all from left-wing organisations at all - the Union of Jewish Students for example is definitely right-wing (they have tried to no-platform Chris Williamson!).
But the really crucial point here is the distinction between free speech and hate speech. Your quotes all refer to ‘groups that wish to harm us physically’, ‘those who continue to threaten or incite violence’, etc. This is an obvious point of both established law and common sense - well reflected in this forum, where all views and discussion are uncensored, but abuse, threats, etc, are not allowed. There is nothing political about this - it’s just good old-fashioned politeness and decency - but in-so-far-as it has a political dimension, the point is that hate speech actually prevents free speech.
In this difficult territory, worth perhaps turning to some really insightful writers, like David Olusoga or Nesrine Malik…