Men wearing dresses, acting like 'women' in plays, musicals, vaudeville etc has been around ever since women weren't allowed on stage, or as actors for that matter. It was a Western culture thing (maybe an Eastern thing as well?) so men filled female characters roles until possibly the early 1900's. As far as I can tell, these touring companies were mainly comedy troupes and became particularly important during WWI, used to entertain troops to maintain morale. American entertainment troupes were similar, and the origins can be traced back to the Civil War. The USO was founded in 1941, but by that time, women entertainers and actors filled their own roles
