In the last two examples you quoted me on I feel like you may not have appreciated that I was talking about the connection between the government (ie the law) and JP's role as a professor. He's free to do whatever he wants as a private citizen. He is also free to say whatever he likes as a prof so long as he does not target a specific student in a discriminate manner. So with regards to him being hypothetically racist, yes the university could reprimand him, but what I was referring to was that he could be accused of breaking discrimination laws as well if, as a professor, he racially discriminated against a particular student. To use a rather extreme example, if he told a kid they were not allowed in his class because they were Asian that would violate the law. Likewise if he barred someone from his class because of their gender expression, that too would be illegal. Though this doesn't legally prevent him from expressing extreme opinions about the concept of race or gender in his classes.

Likewise in the quote that followed (where I mistakenly included an extra "not") the government is only policing this matter of basic courtesy in regards to how it applies to Peterson as a professor and his direct impact on an individual student. Not only is he free to say whatever he likes when not acting as a professor, he is also at liberty (both by law and by express opinion of the university) to say whatever he likes about gender and transgenderism. He could say transgenderism is an abomination, the product of hate and evil fused together. He is just not permitted to single out a student for discrimination based on that prejudice for their gender expression. Likewise a employer or landlord cannot discriminate based on someone's religious beliefs or martial status or age, though they are free to say whatever they like about those same concepts.

Peterson's case for associating 'criticism of fashion choices' and hate speech is, if nothing else, misleading. He can stand at the front of his class and criticize fashion all day long, he just can't single out a specific student and discriminate against them unjustly because of their gender expression. The law doesn't prevent him from expressing opinions about clothes, accessories or makeup.