Whilst the 1954 definition has its faults, it is a good attempt at defining a particular type of music which has special characteristics. Otherwise we are in horse territory.

It is true that the term "folk song" has come to have a wider meaning than this. However, defining a "folk song" as anything which can be heard in a folk club is not only too broad to have any meaning, it doesn't help with defining the popular usage. A pop song may be performed in a folk club, but it is still a pop song. It may have tbe potential to turn into a folk song, but only if it has started to show variations and absorption into a tradition; the obstacle to this is that the original definitive version is usually too widely known for this to easily happen.

For example, Swan Arcade used to do a stunning version of the Kinks' "Lola", which they regularly performed in "designated folk contexts". I don't think anyone, including those in the audience, would think of "Lola" as a folk song.

The problem with the OP's definition is that the audiences at "designated folk contexts" are actually usually fairly tolerant and will accept other genres of music, provided they are performed in a sympathetic way. So a pop song performed in a folk style may be accepted whereas a heavy metal version of a 1954-compliant folk song probably would not.