I remember well the horror of being a manager whenever a customer starts acting dickish or bizarre in some way. You look around for the person in charge, and then you remember it's supposed to be you. Omg, what do I do, make this person stop yelling, what would corporate say here, uh...
I could accept that the manager panicked and made a terrible call. However, it was a terrible call, and people get fired for those.
If it had been me (putting myself back in that headspace *shudder*) I'm almost certain that I would have said something like, "I'm afraid we won't be able to accommodate that request, ma'am" in a bland tone of chilly professionalism. And when the old witch inevitably kept yelling racist bull ****, "I'm sorry, but this is a family restaurant. You're making a scene, and I'm afraid you'll have to leave." Make a note of the incident for corporate's perusal, getting ahead of the imminent bad Yelp review. Give the poor server a quick pep talk and remind her that she's valued. Apologize to any customers who seem disturbed. Carry on.
It's not perfect, but I think it would have been the best thing to do in this circumstance. I'm 100% certain I wouldn't have gone and gotten a white girl, lol. I don't want to unfairly judge the manager from my comfy armchair, but he was hella dumb here.