Some labels & usages have, as noted, been around since the late 1800s and were used off & on, but it didn't really become an issue until people like Cecil Sharp, John Lomax and a few others began 'collecting' and publishing and doing actual field recording in the 20s & 30s. Then they needed some agreed on language so the libraries & book stores and record companies could file things.

Problem is 'folk' is such a neat, handy, short word that it got co-opted by certain people who wanted to shoehorn THEIR stuff into a nice, accepted category.

and off we go!