Here's a few precedents from Down Under to consider, that I came across in my academic philosophising days.
Sex discrimination is illegal, unless you get a specific permit from the relevant minister. Fernwood Female Fitness Centre are a gym network for women only. They managed to get a permit from the minister to reject all males on grounds of sex/gender not fitting their business model.
While discrimination is generally illegal, you can get around it if you can make a good case. At least in Australia. There is a gay bar in Sydney that has done the same thing and is officially and legally gay only.
In Melbourne there is a group of well organized hippie nudists who have a weekly swim meet at a public pool, on a weekday evening when the pool would usually be closed. They cover the cost of opening it for their exclusive use. Something like this may well be possible for your group.
There is also a new invention called the burqini, a swimsuit designed to meet at least moderate Muslim rules - neck-to-ankle coverage, super modest (and I bet it prevents sunburn and skin cancer too!). This might help some of the less extreme Muslims but I believe that the strictest ones forbid men and women ever to bathe within sight of the opposite sex.
Sorry, was I allowed to post in a thread marked "Women only"? I've been having doubts about myself ever since I posted in the handbag thread.