On doing a little further research, the reason there were no protests by parents over forcing their kids to swim naked was because before the 1960s, The American Public Health Association required nude swimming in pools beginning from about 1926 for health concerns due to poisons contained in swim suits.
Of course this was only during the men's period for swimming.
Women were not required to do so during their swim period which makes no sense sense since their swim suits were surely made of similar materials. Of course, I guess they could argue that there would be less poisons in the pool if the men followed the procedure and that it was not appropriate for women to be naked.
I don't know of any high schools in San Francisco before 1960 that had pools so that is why it was never a concern here.