I quote from your post: "The American Public Health Association required nude swimming in pools beginning from about 1926..."
Yes, from 1926 through 1962, the APHA did RECOMMEND nude swimming (for males), NOT because of "poison materials" in swimsuits, but because of waterborne diseases like typhoid, dysentery, and pneumonia, among others. (Some civil engineers also pointed out that fibers from swimsuits could clog pool filters, but this was not a major concern.)
The APHA is an advocacy organization (founded in 1872). It is not a government department, and has no legislative authority. Therefore, they could not have "required" nude swimming.