I am a pilot (not an airline pilot). It is absolutely mandatory for the pilot-in-command to have complete discretion when dealing with passengers on their aircraft. While I may have let this man board my own plane, this pilot-in-command used his own judgement to determine that the passenger presented too large a risk to the safety and comfort of other passengers.

It is completely within his duties to do that. It is also completely within Delta's duties as his employer to question his judgement and fire him for being a racist later.