Asking to be treated with respect by the state and it’s institutions is exactly what MLK did. There is zero difference! One of the ways that MLK persuaded people was with an enourmous march on Washington, DC, and by meeting with politicians, including the President, to demand that equal rights be codified in law. And this still does not explain or excuse why he had a duty to do this despite a messy personal life, but everyone else has to “have their house in order” first. It just shows how flimsy Peterson’s arguments actually are, because even he can’t stand by them.
And we already regulate language extensively in a wide variety of ways. You cannot claim that your product does things that it doesn’t — that’s fraud, even though it’s “only language.” You cannot yell “fire” in a crowded theater because it endangers other people. You cannot threaten to hurt of kill someone even if it’s an idle threat. You cannot call your co-workers by sexually or racially demeaning names. That creates a hostile work place and it was deemed as such in the Civil Rights Act of 1964 — something that MLK advocated for.
Peterson’s whole deal is that he doesn’t like or understand trans people because they don’t fit into his binary world and so he doesn’t want to be encouraged to treat them with respect, because he doesn’t want to. Out of that emerges a whole bogus support system to justify his bigotry.