“not privatize all of the pools and beaches? “
You can privatize all the pools, although it isn’t clear how private agencies could afford to run them. The beaches, however, are federal property up to the mean high tide level and many of the beaches in the NY area are federal National Recreation Area or National Seashore property.
It might be possible to have separate sex areas, though. There are some areas that are set aside for public nudity in the federal beaches, with warning signs for those who might object.