We had that issue up North at our Country Club 10 years ago. The club did not want golf hats in the dining area or bar (in the "Pub", hat were fine). Then the question came up about women. So it was decided no hats in the dining/bar areas except on Easter. (You can imagine some of the discussions) So it ended up, male or females could wear hats on Easter only.
Today's social environment creates more of an issue.............it's not determined if your XX or XY, it's who you identify with.
Stopping there so it doesn't get political.