Read an interesting story that happened to Seth Godin as he rode JetBlue recently - he was really upset about the service but he glosses over the details.  "They could either sit together in row 20 or sit separately) but that they were willing and able to go nuclear with total aplomb".

Can or should a company (like Jet Blue) ban some customers?

"Would it be okay for JetBlue to blacklist this couple? To say, "you guys totally crossed the line, you can’t fly with us any more?"

I don’t think it’s enforceable - without getting into violating some constitutional rights.  Sure, you could create a flag on your reservation system that prevents the person from flying on Jet Blue again, but then the person could sue JetBlue for that - so what you could or should do and what you end up doing are really two different things.