Well, I was finally forced to actually do my own search on the internet. I guess I should thank you?

Most federal laws in the U.S. (e.g. Chamberlain-Kahn Act, Mann Act, Development of the Bureau of Investigation to fight "white slavery") occurred before women got the right to vote. Unclear what year the Supreme Court ruled that "consensual debauchery" was subject to the "immoral purposes" rules, but the judges' decision seems to be unrelated to women getting the right to vote and based on laws passed before 1920. Although the protests of what were mostly though of as women's groups (e.g. temperance movements) were felt to be influential, most states in the U.S.A. made prostitution illegal between 1910-1915; a full five years before women got the right to vote.

More to the original point of my question, it appears that the public opinion against prostitution began to shift around the 15th century due to numerous infectious disease outbreaks across Europe and gained steam with the Protestant Reformation in the early 1500's. The spread of Colonialism throughout the 1600's into the 1700's created another vector of new STD outbreaks causing France and the U.K. to pass formal laws against prostitution, not just on a local level, since those already existed, but on a global level (to include any overseas colonies despite local attitudes toward prostitution) in an effort to regulate return of STD's from their colonies in the third world back to the homeland.

For reasons that should be pretty obvious, communist countries have almost always opposed prostitution for reasons unrelated to moral, religious, or infectious disease concerns.

In almost all of South America, prostitution is legal.

Thank you.

P.S. Mississippi finally ratified women's right to vote in 1984.