He has no issue with gender pronouns, he has issues with the government legislating how people think and speak.
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,”
http://www.thecrimson.com/article/2017/4/11/peterson-talk-dr...