So I listened to the interview. 30 minutes. Nothing he said seemed unreasonable. Seems like he's misrepresented, unless there is more that is missing. Also, he seems to have billions of YT videos. No time for that, but I couldn't find anything remotely transphobic.
No there isn't anythign transphobic about his viewpoint. He does not believe that compelled speech should be written into law. In other words, he does not believe anyone has to right to compel someone else to use whatever pronoun they wish to be identified by. It has nothing to do with whether or not you actually do refer to someone by their preferred pronoun, it's the written into law bit he objects to. As he said, he is quite happy to call someone 'she' if they want to be called 'she'.
A lot of it is to do with 'gender-neutral pronouns' anyway. Most trans people conform to the gender-binary. They are quite happy to be called 'he' or 'she'.
Pretty much. The stupid thing is that he's apparently misrepresenting the law that he complains about. He's created a dystopian idea that he is leading the charge against which doesn't seem to be in the pipe line at all.
Some lawyers claim he misrepresents the bill, but he was advised by a lawyer on the bill who backed his reading of the code. Though it's a shell game with the truth here. The bill itself cannot do all that he claims, but the bill feeds into the Canadian Human Rights Tribunal which then can issue fines and set standards. So it's not the bill by itself, but the other law departments it connects to that create the compelled speech issue.
The Lindsey Shepherd thing is an example of how once put into code, and with the threat of the human rights tribunal, organizations looking to legally cover their ass will view it just as Peterson claims.
You can also look at the Dear College letter in regards to Title IX. The letter is not law and never states to directly take away fair hearings, but the threat of the letter and how it gives activists power lead to colleges violating student rights during investigations.