My mother never would let me swim at the Y because she had "heard that people swam naked there." That was the sixties and turned out to be untrue.
It was true in Baltimore.
An old-time Boston pol told me the public school district used to do physicals at the Boys & Girls Club, which had the same nude swim rules for boys. This guy always got a doctor's warning, because his heart rate was so high. He was early in the alphabet, and before the docs showed up, he and always the boys were wrestling and horsing around, throwing each other into the pool. The other boys had time to calm down. He didn't.
As for Y, my little boy is in Y camp during the summers, and to judge from the number of swimming suits he has lost and/or allowed to rot, there are solid practical reasons for not having bathing suits.