Which FAA regulations require passengers to comply with flight crew instructions?
On the day itself, the captain decides who gets to be on the aircraft when it departs. End of story, full stop.

Not abiding with this falls under the interference provisions you already mention -- or, more elementarily, it is trespass. Local law enforcement will help enforce the decisions if necessary.

Afterwards, if someone who didn't get to fly contends they had a valid and applicable contract from the airline that entitled them would fly, they get to duke it out in court for monetary damages.  How that turns out would depend on a lot of factors that are better discussed on Travel.SE or Law.SE.

The airline may lose in court, and if the captain's decisionmaking was sufficiently egregious (say, "there'll be no [racial slur]s aboard the plane I'm flying"), he may soon find himself out of job.  But the police who enforced the captain's decision on the day were still in the right to do so.  It's not their job to attempt to unravel contract disputes on the spot.