I am sure there are plenty of people with money to burn if they could win such a case and make a point in the national news. In fact, they did and LOST. I don’t think such a case is winnable. Even by a seasoned lawyer.

http://www.nydailynews.com/new-york/judge-rules-nightclub-en...

http://musicfeeds.com.au/news/dude-sues-melbourne-nightclub-...

Even a place which excludes men openly is allowed to operate, though this is borderlin. Lucille Roberts was a successful chain of female-only gyms advertising itself nationwide as just for women.

https://slate.com/human-interest/2018/04/women-only-social-c...