The NPR history department did a story on a Brief Historical Survey of US Bathing Suit Rules (Not the Jewish Ones). Hat tip to KS.
Thank goodness it concludes:
...as the 1930s wore on, restrictions on swimwear began to wear off. Stories about beaches posting dress — or undress — codes seemingly disappear from newspapers. By 1939, the city of Hammond, Ind. — apparently reflecting the relaxing attitudes of many American towns — had thrown all bathing suit rules out the window. "The city will establish no rules on type of bathing suits to be worn," the local Times reported on June 16, "just so bathers are garbed in some fashion."