Some background for the readers: before the mid-20th century, it was normal practice to dress male and female children alike until the age of "breeching" (technically an 18th century term, but handy to describe the phenomenon), generally between 4 and 7, when the boys would start to wear bifurcated lower garments. There could be subtle distinctions made between boys' dresses and girls' dresses as boys neared breeching - an older boy's dress might be styled more like a jacket, with decorative buttons down the front (both sexes' dresses fastened in the back; girls would continue to wear back-fastening dresses until they were deemed adults) and cuffs, or like a kilt.

However, as you may have heard, there was no concept of boy-colors vs. girl-colors, at least not to the extent that there is today. Some publications would recommend particular tones for each gender, while others contradicted them and yet others said there was no distinction to be made. You can find images of boys in blue and girls in pink, but also images of boys in pink and girls in blue and red and every other color. (Infants were generally dressed all in white.)

The shift from gender-neutral to strongly gender-coded clothing occurred, according to Jo Paoletti (Pink and Blue: Telling the Boys from the Girls in America), between 1890 and the baby boom after WWII. One part of this is economic: restricting certain colors (pink/blue) and styles (dresses) to a certain gender meant that hand-me-downs had a smaller audience. Where parents could have previously allowed each of their children to wear the same clothing up to age five or so and then purchased/made gendered clothing, with a sense that boys and girls should always be instantly recognizable, they now had to shell out for two sets of clothing from birth.

But there are also social reasons. In the first half of the 20th century, Western society was also facing a great deal of anxiety about sexuality and gender roles. This was a time when homosexuality as a concept began to be defended, gay people began to come out/have more visibility, and women started to become a greater share of the workforce and dress in ways that challenged certain norms of gender roles (shorter hair, trousers) and standards (showing more skin, wearing fewer layers). By lowering the age of gender differentiation and more rigidly defining the ways in which children performed/displayed gender, society "struck back" against these changes.

In the 1890s, there was also an enormous fad for "Fauntleroy suits" for boys. Based on that worn in the novel (and subsequent play) Little Lord Fauntleroy, it was a black velvet suit with lace collar and cuffs, generally worn with longer hair. (You can see a couple of examples here.) The character of Cedric Erroll, the little lord himself, was not at all effeminate by the standards of the day - he's brave, strong, and active, and was generally considered charming. Even though it was thought of as a good book to give children due to its moral lessons, it still won 77% of the vote in a popular magazine's poll for favorite novel of those under twelve. The pushback began against the suit itself rather than the character or book, although the title itself is now used as a synonym for fussiness and effeminacy. Critics complained that women were blind to the fact that their sons' mischievous natures would not be erased by the suit, that they were reducing their sons to fashionable accessories or inculcating undemocratic and aristocratic standards, and that they were preventing their boys from indulging in the more active, dirty outdoors play that was coming to be seen as "natural" and necessary for male children. It seems very likely that the coming-of-age of the Fauntleroy generation resulted in the first strong shift away toward more strongly gendered children's clothes in the 1900s. (For more on the Fauntleroy fad, see Kristen Stewart's Little Lord Fauntleroy: The Defense of a Fashion Victim.)