Is insisting that people say "Gulf of America" similar to insisting that people use "they/them" and other "preferred pronouns"?

I see that "On Tuesday the White House broke with decades of precedent and blocked Associated Press reporters from attending two of President Trump’s media availabilities. The AP said it was blocked because it hasn’t changed its stylebook entry for Gulf of Mexico to 'Gulf of America'" (CNN).

Say it my way or face consequences.

The consequence here is the loss of a great privilege, the access given to the small group of reporters who speak directly to the President. But it made me think of the pressure that has been applied to ordinary people to say things in a way that is dictated by their political antagonists.