You may have read Jonathan Chait's opinion piece on the way language policing is perverting liberalism.
I read the piece a few times, but I'm still not clear on how his different examples relate to the topic he wishes to address, and I'm not 100% clear on what that topic is (freedom of speech issues? what hurts the liberals? what hurts Jonathan Chait?). They span a range of cases, from wrecking someone's house because of what a person wrote, via the demands for trigger warnings in some college courses and campaigns to have controversial campus speakers banned, to an author being strongly (if humorously) criticized in a Twitter hashtag.
On the first and last of those examples almost everyone would agree: nobody's house should be attacked because of something that person said and honest criticism of an author's work on Twitter is a legitimate form of debate. The case of demanding trigger warnings (not a very widespread phenomenon, as I understand it, and criticized by several feminists) isn't about suppressing speech as such though I guess it could have a "chilling" effect on the courses of the professors responsible for reacting to the demands. That leaves the question whether one should try to ban speakers or speech on campuses. Those attempts are carried out by both the left and the right in this country, though in slightly different forms (e.g. firing a professor versus getting someone's invitation to speak cancelled).
Indeed, Chait's piece has so much material in it, much of it not of the same general species, that I had great difficulty making a straightforward summary about it.
Glenn Greenwald's response links to several other responses which you should read if you are fascinated by the topic of how we speak and do not speak, whom we listen to and do not listen to, and what it is that some people experience in online debates and how they interpret those debates. But I agree with Greenwald that Jill Filipovic's tweet on all this makes a good point:
Julian Sanchez writes about some of those issues. An example:
Let’s take it as given that this is not the case, and that any subjective chill experienced by folks like Jon Chait is not usefully understood as a problem of social justice. We can grant all that and still ask: Is there something unhealthy about discursive norms that lead to substantive self-censorship, even by the obviously privileged? Not because these norms constitute an injury to the reticent privileged, or interfere with anyone’s sacred right to unfettered self-expression, but because they yield less robust, less interesting conversations?
Think of Solomon Asch’s famous experiments in group conformity, or the broader social psychology literature on information cascades. The problem isn’t so much that some precious snowflake’s project of expressive self-realization has been constrained, but that constraints deprive groups of deliberative input that can help them make better decisions. When the constraints are on the order of “don’t use sexist or racist language,” probably nothing of value is lost. When the constraints include “under no circumstances express any skepticism about any claim of sexual assault,” to pick a salient recent example, you may end up with bad journalism that hinders the ultimate goal of getting society at large to treat survivors’ stories more seriously and respectfully.
This is an important point. To give another example, suppose that a social activist group is preparing a statement based on six cases of labor market discrimination against women and/or minorities. Suppose one of the cases, the sixth, isn't really like the other cases. It's different and weaker and may not be an example about discrimination at all. Suppose you think so, but say nothing because of the fear of group ostracism*. Then the list of the six cases goes out and conservatives tear that sixth iffy case apart and imply that all the cases on your list are like that one.
So certain group norms can affect not only how robust a conversation is but even the outcomes from that conversation.
*The fear of group ostracism is probably less if people meet in person than on the net.
By the way, I found the juxtaposition of rowdy public discourse and the question of ostracism interesting in the various takes. They range from essentially arguing that if you can't take the heat stay out of the kitchen (which are even hotter for the more oppressed groups, by the way) to wanting all online mockery to cease because it's a form of language policing. So what is free speech here? The speech you like?
I may be mistaken about that. But it was one of the sticking points I had with Chait's arguments.