> Senator Rand Paul has said that the Deep State exists. Is he a nut also?

Yes.

"He has cautioned in the past of a plan to create a North American Union with a single currency for the United States, Mexico and Canada, and a stealth United Nations campaign to confiscate civilian handguns. He has repeatedly referred to the “tyranny” of the federal government."

He's a strong libertarian which is, by definition, wackjob territory.

"The Deep State" aka lifelong career civil servants doing their jobs and investigating criminals.