I was curious if a case could be made for First Amendment rights, but I just re-read it... "Congress shall make no law regarding..." I guess Executive Orders can bypass all of that.
Just like a private company can have speech codes without running afoul of the first amendment, so can the US Government for its employees. That's all it is - not some law, but an employer mandate. The first amendment applies to law governing speech.
Weird that it's EPA-only, though.