Here's an interesting story, via someone I should recognize but missed, on women's lib, arguing that the advent of bicycles changed things and liberated women. It mentions riding sidesaddle. Now one could assume that the Victorian Age constraints on women were focused on the Anglo-saxon world, given Queen Victoria reigned over the British Empire and we concede that much of American popular culture followed the Brits. (Anyhow, that's the way my mind would work.)
But, separately there's an article in the NYTimes on Mexican rodeos ("a charreada") in the U.S. as Mexicans incorporate some of their traditions in their U.S. life. One of the features is a parade of women in petticoats riding sidesaddle. Whether Hispanic culture was as Victorian as U.S. was I don't know.