I've recently written an answer on this topic, which I'll share here!

Actually, yes! Penmanship has been gendered for a long time.

In the eighteenth century, there was actually a number of different "hands" that people might learn, based on their rank and needs. In Penmanship, or the Art of Fair Writing (1770), Joseph Champion lists 17 different options: round hand, ditto text, Italian hand, running hand, engrossing, secretary, square text, German text, large court hand, small court hand, running court hand, sett and running, Chancery, church text, Old English, round Roman or new print characters, and italic print characters. Of these, some are meant for business use (a running hand or round text) and some specifically for the legal profession (ditto text, engrossing, and secretary); the rest are "ornamental" and meant for inscriptions and dedications in printed books and the like. Women, however, were expected to focus on the Italian hand - they did not typically get involved in the paperwork aspect of business and were not allowed in the legal profession. The Young Clerk's Assistant, or Penmanship Made Easy (1787) shows a number of different hands, all of which look fairly similar to a modern eye; you can see the subtleties of this in the page that compares round-hand and Italian characters. But they are different, particularly in the capitals, and you can see how people of the time might have distinguished masculine and feminine handwriting at a glance.

This division continued in the nineteenth century. Although a number of writing "systems" were devised - most famously the Spencerian script, devised by Platt Rodgers Spencer in the 1840s, but similar ones were named Appleton, Barnes, Merrill's, Gaskell's, etc. - it was still common to find people discussing round, running, and ladies' hands, as well as engrossing and Old English/German scripts (essentially Blackletter fonts). By the early twentieth century, perhaps because of the rise of the typewriter as an impersonal method of committing words to paper, the focus seems to have shifted to a system of writing that was at least not deliberately gendered: take, for instance, this Popular Mechanics ad for a writing style that could teach ladies "as successfully as men", which was repeated many times in that publication in the 1920s. This style looks more like the old nineteenth-century ones, however, and it was on its way out: the Palmer Method of Business Writing was being adopted at this time for teaching to children across the board, at least in American schools.