The government doesn t have constitutional rights. Constitutional rights belong to the people and restrain the government. The people s right to speak may not be abridged. Government officials speaking, in their official capacities, may certainly be abridged. Indeed, it often must be, precisely to restrict officials from abusing the state s monopoly on violence to bully citizens into serfdom.
It is obviously un-American and unconstitutional for the government to develop a hit list of citizens to mute in the public square through secret pressure on communications monopolies beholden to the government for their monopoly powers. There is simply no way it s protected speech for the feds to use intermediaries to silence anyone who disagrees with them on internet forums where the majority of the nation s political organizing and information dissemination occurs.