Do folks really believe that's what gender-balanced work places are like? I used to work at a large New York law firm where 40% of the lawyers were women. All of my teams were mixed, and out of happenstance I spent the bulk of my time working for women partners. Nobody was "terrified" because everyone knew how to act like a professional adult.
The people you're describing of being so terrified by these events or adopting unofficial policies against women already had a misogynistic bent. They were already a problem. Them using an event like this to justify their anti-social behavior is typical, but it is not the cause. They weren't accepting bastions of equality until they were frightened into sexism. Putting them on notice isn't the end of the world for anyone.
Whether we appease bigots or confront them, some people are going to be assholes until they die. I'd rather confront them and leave no question about which way the world is going.
Why are you so scared of women?
We all know this is how Directors and VPs and the like think, we just don't say it.
It's really not.