There have long been people on the political right, especially those associated with the Christian right, who want to restrict your expression of ideas they do not like. For the atheists among us, words like "blasphemy" and "sacrilege" quickly come to mind as some of the more disturbing examples of this. Even today, there are conservative Christians who would welcome criminal sanctions for those who dare to criticize their religious beliefs. We don't have to guess at this; some are perfectly willing to advocate for it. And of course, there are plenty of milder responses designed to restrict the expression of other ideas they find objectionable.
Efforts by people on the political left, especially among those associated with the authoritarian left, to restrict your expression of ideas they do not like are newer. When it comes to religion, some seem bizarrely selective (e.g., it is perfectly acceptable to criticize one religion, but criticizing another is "gross and racist"). We do not hear as much about criminal sanctions from this group. They seem to prefer a combination of public shaming and mob outrage aimed at harming the target's employment. Evidently, they see it as their right - or even their moral obligation - to destroy someone's reputation and financial security merely because they are offended.
I never thought I'd see the day when one of the things the far right and far left would agree on was that people who say things they don't like need to be silenced. Obviously, they differ greatly on the things they find objectionable. The manner in which they seek to punish offenders differs in some ways too, but there are plenty of areas of overlap (e.g., the boycott). Where things match up is the belief by members of both groups that there are certain things others should not say and for which they should be punished if they do say them.
We have all read the reports of polls showing a decline in the support for free expression among young people, and this seems to cut across political lines. It has been an issue on the right for some time; it is now clearly an issue on the left too. I find this both disappointing and scary. People who argue that others should have the right to express their views, no matter how objectionable such views might be, seem to be members of a quickly shrinking minority. Across the political spectrum, one does not have to look hard to find people who are in favor of prohibiting speech they do not like.
Free speech has always struck me as a core democratic value. More than that, it seems to be so closely tied with freethought that I have a hard time imagining that one can exist without the other. If we are not free to encounter views we find objectionable, I am not sure how we ever make it out of our bubbles and fully engage with others.
I am horrified by efforts from religious fundamentalists of all faiths to criminalize the expression of what they regard as blasphemous speech. And I am seriously disappointed by efforts from the secular left to deter speech they find objectionable through Internet vigilantism, especially when the stated goal involves the financial ruin of the target. Those who feel similarly need to push back against both, and I think this transcends politics. I do not have to become a conservative to oppose this aspect of what the left is doing, and conservatives do not have to become liberals to oppose this aspect of what the right is doing.