Odetta Holmes and Rhiannon Giddens both trained in singing for opera (Rhiannon at a more advanced level than Odetta) but would sing folk songs like folk songs. Rhiannon Giddens is especially versatile and sings in various styles. So classical training doesn't necessarily prevent singers from performing in a more natural style if they choose to do so. Sandman also says that, but didn't give any examples.

One positive side of singing songs in an "unauthentic" style, whether it be art song or pop song, could be that some listeners will go search out the roots of the song and learn more about folk music.

I was thinking this week about folk song and art song, but in a different context than classical music. I had lyrics for a waulking song - a work song for fulling the tweed - and was looking for a recording. The first recordings I found sounded nothing like a waulking song. Would you think that track 19 on
https://archive.org/details/GaelicSongsOfScotland-WomenAtWorkInTheWesternIsles/ is the same song as Alasdair Caplin - Sheòl am bàta ?