Jordan Peterson strikes me as an anti-trans bigot and all-round meanie. I sympathize with the trans and queer activists/revolutionaries who're giving Peterson a hard time. On the other hand, this new bill and Canada's anti-discrimination laws indeed constitute oppressive censorship. As often happens, both sides are wrong.
As far as language goes, gendered pronouns are ridiculous to begin with. Why do pronouns need to be gendered? Trans/nonbinary/genderqueer/etc. folks are just doing our best to negotiate the goofy gendered language that doesn't suit us. You can ignore our preferred pronouns as you can ignore anybody else's, but doing so adds, if only slightly, to our marginalization. I don't recommend it.