"There was a period of time in the world when women rode sidesaddle. The first time in America that people saw a woman riding astride was in 1852, and everyone thought it scandalous."

Is there a source for that?

I suspect that what is getting overlooked here is both the rarity of horses and that there were some fairly rigid class structures.

Throughout much of Europe and the early colonies horses were expensive and extravagances limited to the rich. Oxen or cows were far more common, and practical, for farm work or peasant use. And to make an ox into a conveyance one used a cart or wagon.

Those rich enough to afford a horse were also the most likely to be scandalized if their high bred women rode split-legged. There may have been poor women or girls rode in the normal manner but history is seldom written by or about the poor. History concerning itself with anything but the rich is a new phenomenon.

Which may be why it is assumed all women, or at least all the women who counted, rode side-saddle. If at all. Between the many petty coats, hoops and other female impedimenta riding on a horse was obviously something of a major PITA for women. So likely seldom done. There were plenty of two and four wheeled conveyances available that could be easily harnessed to a horse. Those rich enough to afford horses likely had servants to set up a carriage.