Not only are they legal, many male only city clubs exist today!
https://en.wikipedia.org/wiki/List_of_gentlemen%27s_clubs_in...
Male-only country clubs also exist although are slightly more controversial and less common, such as Burning Tree, Garden City, Butler National, Augusta National (until the last ~10 years), Pine Valley (until the last few years).
The unfortunate reality for most of us is that these places are among the most desirable and hardest clubs to be accepted to in the world - and we probably wouldn't get in.
Maybe it's time start new and less desirable clubs for the common man.
A lot of new clubs are currently being founded in NYC and London in particular.
They're expensive to run, so they often target a wealthier demographic who can pay.
> many male only city clubs exist today!
Em. Nearly all clubs on that page that I checked are open to women or no longer exist.
Several appear to be women-only social clubs, placed on the page by mistake.