This could be a very serious issue that could reverberate through the entire private club industry and could change the way they do business forever. Or it could be that switching to a woman and taking a bunch of hormones has driven this already nutty person further out of his/her fucking mind.
First off, if you are a member of a club you have signed a bunch of membership papers that govern behavior, and if you start running around the clubhouse in a clown outfit with a plastic axe, you will be asked to relinquish your membership. Legally, this is no different. The club has the right to discriminate. It would have been a far better legal issue if he/she had hooked up with a black or Mexican and tried to keep membership as a gay man. Now there would be a good one with which to argue discrimination. Equal protection under the law can be applied to public places.
And by the way, sir/madam, you had no problem when others different from you (at the time) were excluded from your grandfather’s still-racist-piece-of-shit private club. Those who disdain these types of clubs across the country can only chuckle and thank you for making this national news. The best part of that story is of course that this proud German-American man/woman is being represented by a lawyer named Silverman. Now that is a bit of progress to be proud of.