I'm sure people have encountered the following;
A level Music project - write a string quartet in the style of Haydn.
Now a successful result will be clearly identifiable as classical music. Despite the fact that it is not from the (relatively) short period in history when this style was in vogue. You can also write Baroque music even though it is a long time since the genre 'died' with J.S.Bach. (1750 for musicologists)
Similarly it is entirely acceptable to write a string quartet in the style of Bartok and nobody is going to consider it 'classical'. Surely 'folk' is in a similar tradition to the 'classical' tradition? If you write a song in the style of an early 19th century broadside (taking care in your use of words and phraseology) you are not going to create a 'pop' song or a 'blues'. Why is there such confusion over style and genre?