The firing is part of the injustice. If Applebee's had said "Wow, that is unjust, what the hell" then Applebee's comes out of this on the side of someone fighting a perceived injustice. As it is, much less so. I'd hope that most people would not be swayed by the pastor's argument- I would be surprised, even, if Applebee's hasn't just planted themself squarely against the majority.
I think that you are projecting your values on to Applebee's, meaning that you're assuming their target demographic are people like you. However, it is far more likely that their target demographic are the type of people that would have more empathy for the pastor in this situation rather than the waitress. Therefore, if we are thinking of the best interest of the organization that we run, the best decision was to fire the girl. Most people who empathize with the pastor, will see this as if someone that filled out a "comment card" and had that comment card displayed on the Internet for all to see. Most people don't care about details, they care about perception. People want to know that the customer is always right, even when that customer is a D bag. You may read this and say I'm never going back to Applebee's ever again, but then the chances are you were never a big Applebee's fan to begin with. Now if a big Applebee's fan reads this and they think to themselves I can't believe they did that to the poor pastor, and made that privacy thwarting waitress a hero...Then, you've lost a customer.