While I was looking to get a membership at a hot yoga studio, this one is clearly not the right fit as if you have a husband, brother, son, etc waiting on you they will be told to leave (literally a few steps over, this studio is open to the Mall).
Women only “in-class” totally makes sense, but having sexist behavior against anyone is never ok. I’d make the suggestion to add walls and doors to better create a closed off space to the mall, train your staff in how they deliver their requests, and add a chair or bench in a place for those support persons to wait.