Sure, why not? It is illegal for police to enforce laws on certain public officials in certain circumstances. IIRC members of congress can't be stopped for a traffic violation on the way to a vote, or something like that.

The ancient Romans didn't allow prosecution of some public officials while in office for a similar reason. Their courts could too easily be abused as a political tool.

It's not unreasonable to leave public officials unmoderated while they're in office.

The real problem here is that we're letting private companies make the decision. We should pass a law that requires unrestricted free speech on any platform of a certain size. And then give users optional moderation tools. Users could toggle a button that says "Show me fact-checking along side controversial topics" but it would all have to be opt-in.