I used to not mind Peterson because he seemed to help out young males find some direction in their life, but then he found out arguing with transpeople about pronouns made him more money so he let himself be adopted by the far-right.
I don't think this is a fair characterization at all. The issue with pronouns is just a microcosm of a larger issue, which is not just the erosion of free speech, but the influx of compelled or forced speech, which is insidious and must be named and stopped early lest it gain more of a foothold.
As for the alt-right - if you're going to make the argument that some group liking their interpretation of what you've said means that you're one of them, you've got an uphill battle ahead of you. It's plainly illogical to assert this.
Postmodernism and Cultural Marxism
What really is the difference between between ex-Googler James Damore and the young man holding the sign saying "Communist Jews behind Race Mixing" in the civil rights era. Both seem like respectable members of their communities. Yet both think that social progress is actually a plot by evil-doers to destroy society because that is what their elders have taught them.
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRlQquk...
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcTcWkHj...
(Links via Google as some of the images are hosted on rs isn't sirescele rating "the good old days")
He never refused to call anyone by the pronouns of their choice nor he ever said that he wouldn’t do so.
Go to ~9:30 in this video: https://youtu.be/O-nvNAcvUPE
He claims that he wouldn't use preferred pronouns even if there was no law mandating it.
I'm not condemning this choice, just pointing out the falsehood.