No, it isn't. Liberals and leftists have authoritarian tendencies at times. The current cancel and censorship culture is s leftist/progressive phenomenon. I notice that it tends to go back and forth in America as to which side is pushing for more restrictions in expression. It used to be the religious right and now it's the PC SJW left.
Yes, liberals can have leftist tendencies; the Weathermen of the '70s, for example; but "cancel culture?"
Cancel culture is a youth dominated, online phenomenon practiced largely by those who find it easier to criticize than correct. It's not a 'progressive phenomenon.' It's a right-wing trait -- intolerance -- manifesting in a largely liberal demographic -- though Donald Trump seems to be its most active practitioner.
“That’s not activism, That’s not bringing about change. If all you’re doing is casting stones, you’re probably not going to get that far. That’s easy to do.” -- Barack Obama.
Both sides advocate 'restrictions', but the Right promotes symbolic values and restrictions, based on foundations like ingroup loyalty/nationalism, authority, and sanctity.“ The Right promotes conventionalism, regardless of harm, while the left tends to promote restrictions on activities that cause actual individual, social or environmental harm, though, admittedly, there's a recent tendancy for vindictive swiping at 'disloyal' symbols.
Denigrating 'social justice warriors? What's wrong with social justice warriors? Don't we honor Frederick Douglas, Susan B Anthony, Martin Luther King, Gandhi, &al?
This is another twitterstorm from the Right trying to question the motives of those promoting values most of us agree with.
Social justice warrior - Wikipedia