What some conservatives fail to realize is that often their critic is laden with offensive speech, prejudice, or straight-up calls to violence.
I was talking to this guy, and he was lamenting how he does not feel comfortable airing his conservative opinions at work due to the threat of HR. But HR focuses on harassment, bullying, offensive speech. If you could, say, air your grievances with the LGBT in a way that was not homophobic, nobody would really have an issue. And you can, actually, in infinite ways - the left does it all the time to themselves. But conservatives struggle a lot with this and typically can't do it. And that's where the problem is.
Just look at someone like Trump. Yes, he's a republican, but that's not the focus. Compare and contrast how he commonly speaks about women to how Kamala or Walz speak about women. One is OK in the workplace, one isn't. Not because of left or right per se - but rather because one is insensitive, and the other isn't.
You can absolutely critic the left in such a way that does not devolve into identity politics. How many on the right do? Almost none. No, instead they talk nasty, say vile things, use slurs, etc. That doesn't fly in every circumstance. The solution is to be professional and critic with rationale, not critic someone's race, or sexuality, or gender, or their weight, etc. And, certainly, do not call for violence. Conservatives seem to struggle with that too, particularly online.
This tweet[0] was the kickoff point as I recall. I don't really think that getting banned pending deleting the tweet is that egregious. It's one thing to have non-woke opinions and argue for them. I don't follow Jordan Peterson, but I imagine he had posted many times on transgender issues, before he posted the offending tweet.
The issue seems more to have been specifically calling out specific persons, "criminal physician", Elliot Page, in a way that could be construed as inciting to violence
[0] https://nypost.com/2022/06/30/twitter-suspends-jordan-peters...
Thanks for pointing it out, will fix.
So no, he’s not fighting against censorship.
Only someone extremely divorced from reality or wearing extremely partisan blinders could believe this.