No, that's not at all what he's known for. Jordan Peterson is a psychologist and professor who is known for refusing to abide by a law that would force him to use pronouns that students ask him to use. He has very much focused the discourse on the law itself, and what impact it has to free speech if he can be fined, potentially be sent to jail, just because he refuses to use the words others want him to use. Even when confronted by outraged individuals, he has always remained calm and tried to stay on the facts of the issue, not make it about individuals.
Surely, he does not deserve having his opportunity to speak about an issue he thinks is important taken away from him by this kind of mob action.