Maybe it depends on where you live, but no probably not illegal, just incredibly frown upon. I am member of a mens only sports club. We do have a few women, who we sort of had to allow as members, because they had no where else to go and we felt bad about that, but that only for one special program.

If you mention that the club is men only, some women becomes really aggressive and instantly want to become a member or have our public subsidy removed. The only fucking way to calm them down is to point out that there is a women only club right next door. Men doesn't try to invade spaces created for women by women, but women sure as hell cannot leave a mens only space alone. It triggers something in small group of women and they become obsessed trying to force their way in or have the thing shutdown.

You can have a private club with gym equipment that is exclusively for men. But when you're a business open to the public you cannot discriminate based on certain characteristics. Bob's Burgers can't sell just to men. But Bob's Boys Club that happens to have a kitchen which sells burgers to its "private" membership can absolutely keep women out.