SS, I do understand what you're saying. But you were asking for a definition. What I'm trying to get across is that if you say that "folk" can encompass absolutely everything, then it fails as a definition, because it doesn't tell us anything about the music except the context in which it is performed on a specific occasion. To say it can be "folk" as well as jazz, or classical, or hip-hop doesn't help us to recognise a piece of music as being "folk" - which is the purpose of a definition.

Do the George Formby uke-players or classical guitarists really believe their music is folk, therefore they go to a folk club to play it? My guess is they think, "OK, this isn't folk, but if I go to that particular folk club they'll let me play it anyway."

What you have done is to define the music policy for your club. By extrapolating from that to claiming that all music is folk music you are implying that all folk clubs should have the same policy, and that any "folk club" which turns away the uke-players or classical guitarists has no grounds for doing so.