I think that it is a totally different situation if a person privately asks you to speak to them in a way they feel that it is right to be spoken to and when you are forced by an ideologic idea to obey a command.
I wouldn’t like to be called “miss” with over 50 and if anybody does it I would consider how they mean it (you can say it in a caring manner or in a devaluation attempt) and if I feel the other wants to express their supremacy I would protest against it.
So if somebody doesn’t want to be referred as HE or SHE, this is ok as long as they ask it as a kind request (not a command) and nobody will oppose this request, Jordan Peterson for sure would respect that. He is totally right to oppose the demand, which is enforced and combined with the threat of punishment, to use certain terms which are part of an ideological system.
We had “Heil Hitler” and the respective movement demanded in Germany, we haven’t yet overcome the impact of this forced speech and behavior. It is totally right that Peterson opposes the beginnings of a process which will inevitably lead to unbelievable damage and suffering which impacts many many generations — as you can see in Germany. I just wrote an article about that, in case you are interested.