I know you weren't asking me, but I wonder if equating this to a truly private event is quite the right anology.
Let's say that instead of going to my company's annual Christmas party, I decide to organize a separate, segregated one this year ... and further suppose there are enough boobs at my company that it becomes a pretty big one, say a whites-only Home Depot party, or whites-only IBM party, or whites-only Exxon party and it makes the press as such. As a shareholder, wouldn't you expect the company to at minimum issue a clear statement of policy on the matter? Would it matter if the party was held offsite, or if employees were buying tickets? I submit not. Remember, all employees are invited, except for the black ones of course, and we're not calling it a private cocktail reception, we're calling it (e.g.) the Whites-Only Home Depot Christmas Party.
By the same token these kids are having the Taylor County High School Whites-Only Prom. Not a private party at a friend's house ... a prom. This governor is the CEO of the state, the kids attend a taxpayer-funded school in his state, and he should act like a leader and not a wimp. No one's asking him to send in the Marines and forcibly shut down the event. Just to make a clear and unequivocal statement of policy ... it's called leadership, and his stakeholders (taxpayers) deserve that much.