I just heard this for the first time, and I'm surprised that I haven't heard of it before. Someone mentioned it in passing on a podcast I listen to and, after some quick Googling, it seems to be true. It seems crazy to me that this was the case, and that I had never heard of this until now.
Is it true that most public swimming pools (including school pools) enforced a rule of nude-only swimming? What was the reasoning here? Also, what prompted the cultural shift away from this? It seems to be counter to the typical trend of society becoming less modest over time.
Yes, nude swimming (at least for males) was commonplace in schools, universities, and YMCAs all across the country. Pools or bathing times were segregated by sex.
The official reason was to eliminate problems with mildew if damp suits were stored overnight, and to avoid problems with fabric threads in the pool filters. The American Public Health Association recommended nude bathing for males in their 1926 standards handbook. Not until the 1960s were quick-drying nylon or similar swimsuits widely available. Same-sex nudity wasn't unusual at the time, when rural boys still skinny-dipped, and when soldiers, sailors, and athletic teams showered or bathed in groups. Some teachers and youth leaders viewed group nudity for boys as a part of growing up and as preparation for military service. Same-sex nudity seems to be an area where American society has become much more modest since the 1970s.
This Chicago Public Radio report gives more detail on the nude-swimming requirement in Chicago public schools.