I don't pay a lot of attention to popular academic figures and their arguments, but I saw the Peterson interview and he didn't seem like a dipshit. He stated his positions very well and they seem reasonable.
I don't think being against compelled speech law necessarily means you're anti-trans. Sure, he could be using the law as a shield to hide sneaky personal bigotry. He didn't feel like that sort of person though.
I mean if there was suddenly a law that required all citizens to start the morning loudly proclaiming "pedophiles are disgusting human beings," protesting that law doesn't mean you support pedophilia. It's the same shit as bills pushed through congress with patriotic riders so congressmen can say "you don't hate America, do you?"