I don't like that phrase. Because it's extremely vague and implies that things other than physical violence could be a focus of suppression. Intolerant opinions and speech are not and should not be policed in any meaningful way. The free and open exchange of ideas is crucial to a free society. Even those that are "intolerant" or offensive.
And, after seeing what happened over the last couple of years, I wonder how far people these days would take "intolerance of the intolerant"? Can a person who is known to be "intolerant" be banned from a grocery store for no other reason than their opinions? Can they be banned from all grocery stores? Should they be? Should they be fired from their jobs? Should they be harassed whenever they leave their house?
There are way too many ways to abuse the notion that you should be "intolerant of the intolerant".
The irony is that mainstream platforms tend to censor responsibly (even if false positives tend to occur due to the use of bots), while free speech absolutist platforms like Parler would ban you for merely having a different opinion.
The other irony is that free speech absolutists are responsible for nearly all the terror attacks in the United States. The harmful ideas of these absolutists are rejected by society for a reason, but this was the case even before the internet. Freedom of speech is not freedom of consequences.
HN, etc. really shouldn't be "platforms" moderated by a central entity, anyway. If I like Dang's moderation, I should be able to pick and choose it. Maybe there's another potential moderator out there whose sensibilities line up more neatly with my own; I should be able to choose their moderation, too.
Decentralized/splintered moderation, that's what we need.
(I've never been on Parler. Do they actually ban people for disagreeing with them?)
(Is it possible that rejecting people from society makes them more likely to be violent?)