I think Dusty hits it square in the middle.
But an exploration of the edges brings me to feel "folk" vs "some other kind" is notional, communal, and somewhat conventional —and more than a bit bizarre and ultimately uninteresting. I remember the '90s, for instance when arguments raged about the 'rightness' of putting a 6-1/2 fret on a dulcimer. The addition robbed the dulcimer of its folk status for some people, and cast it into some undefined state in which they seemed to imagine the proponents wanted to play chords and render Broadway hits music, which outraged them.
And that did come to pass! And some dulcimers are now commissioned as chromatic, not diatonic instruments at all. Blue Grass, jazz, renditions of classical music are arranged for dulcimers, either diatonic, altered diatonic or chromatice. DF#A is a well-known tuning scheme for playing Broadway musicals.
Another such edge is the status of the banjo, the ukulele, the African kalimba (thumb piano).
There are serious stylists and accomplished masters of all these instruments, yet only a few can walk onto a stage for an evening's solo concert and come away with much more cash than enough to pay their hotel and travel expenses.
That seems to imply another 'edge' to the consideration of whether an instrument is 'folk' or is somehow otherwise meant for 'serious' music —in other words, music people are willing to pay $50-$100 for a ticket.
In the world of rock, pop music, currently, people are paying truly fabulous amounts for leading singers and bands, while other very worthwhile, serious musicians keep squeaking by financially for the love of the music. Yet no consideration is in evidence about whether they are 'folk performers' or not. Is what Taylor Swift sings 'folk?' Nobody cares about the answer.
In sum, I think the love of the music is a much more interesting way to consider an instrument, those who play it, and the breadth of its repertoire, than whether it is a folk instrument. In the end, isn't any instrument available to and actively used by ordinary people a folk instrument?
BTW, a good friend of mine is a master of the hammer dulcimer. She made her first mountain dulcimer in my basement—while playing the French horn in high school. And she may still have a French horn. I'll have to ask her sometime.
updated by @dwain-wilder: 05/31/24 05:09:35PM