No matter what airline, the Captain of the flight can refuse anyone service on HIS aircraft, and have them physically removed. He does not have to explain, justify, or get permission from anyone, he has that authority.
For anyone that can not accept this, they need to find another mode of transportation.
Is the same true of a bus driver, train conductor, taxi driver, etc?
No he doesn’t
Show me the FAA reg that says he does.
You won’t find one.