Earlier quoted context omitted.
Depends on how a judge rules. You could be required to find another venue or to admit women regardless. Either way, the fact that it is a private rule means it is not a public law. The government doesn't have to abide by laws you just made up for yourself on a whim. If I say "no shoes allowed on my private property" the police aren't forced to comply with that, so why would a government official at an event be requir…
The government official isn't the police, but even more so, I'm not talking about the government official, but the random public who attends. I can say they aren't allowed on my property at which point it is a crime for them to be there.
If you're the gatekeeper for who can enter and leave, it wouldn't make sense to call it a public event.