"The club says its policy is to prevent prostitution, avoid distracting men watching the dancers and prevent domestic incidents."
The policy may not be legal under civil right law, but I appreciate that the club is trying to create an environment free from harassing wives, GFs, or their agents. We have had some female members who enjoy strip clubbing solo or with girlfriends, and I understand that their motives are pure, but nobody wants to see Fuck you, Jackie! [RIP] situation explode next to the VIP rooms.
I also believe that private businesses should have a lot of latitude in determining how they want to operate their business. Obviously, we need to ensure that people are not discriminated against because of race, gender, or creed, but businesses should be able to abide by accessibility within policies that match their own creed. A bakery can serve cakes to homosexuals, but not be made to put homosexual-promoting messages on their cakes. A strip club should be able to bar solo women, but allow in couples or groups which are mixed gender. The women even admit that they weren't their as true patrons, but only to look for a woman that resembled the other? That doesn't hold water.

