[...what authority does he have to issue an Executive Order to a private business?”
The answer is Trump has no authority to dictate to a business. What Trump DOES have authority over is the law enforcement apparatus; so if you want to conduct yourself as a ‘Platform’, you will be treated one way, if you begin to act like a ‘Publisher’, the laws are applied and enforced differently.
Trump will direct he law enforcement activities as it relates to the legal protections Twitter and Facebook have heretofore enjoyed, but have put in jeopardy.
Facebook and Twitter will now enjoy legal exposure for their actions.
what authority does he have to issue an Executive Order..
Isn’t the FCC part of the executive branch?