I admit I've not been following his work closely but has he brought up these issues on any other topic than gender pronouns and "SJWs"?
A quick search also suggests he does have actual transphobic issues -
> At the event, Peterson outlined his criticism of transgender people, arguing that the idea that biological sex and gender were independent quantities was “wrong.”
And misogyny issues -
> “I think disciplines like women’s studies should be defunded,”