The Rumsfield case is literally on point: the government cannot force a private party to present government speech. I don't know how much more on point than they can be.

Twitter is not a legally recognized method of presenting Official Statements, as a matter of law (which sets forth the prescribed methods for making Official Statements). They have no responsibilities to present Official Statements, which means they can "impede" access to those statements on their platform all they like, in whatever manner that takes, from simply deleting such posts to providing fact checks to outright editorializing against the official statements.

As noted, I suspect this is not a 1st Amendment issue as the "speech" is present regardless and you have organizations, not necessarily people.

I don't understand what you're trying to say. This is definitely a First Amendment issue...even the White House acknowledges that this is a First Amendment issue. This order is entirely about trying to violate Twitter's First Amendment rights as a private non-governmental organization.

> Twitter is not a legally recognized method of presenting Official Statements

The Trump DOJ disagrees. Further, the ruling that he had to unblock people on Twitter established exactly that. He had to unblock people because he's making statements about government policy.

Therefore, them muting/hiding/blocking him is impeding access to official government statements.

Further, once they mute/hide/block some of his tweets, they're presenting some but not all.

They would probably be safer to allow all or none. This middle ground is editorial control over government statements which is a bizarre middle ground.. imagine a major announcement or policy change not being reported? Or actively being quashed?