This discussion is bedevilled by differing assumptions about what the words used mean.

For example a club that only books singer-songwriters (who presumably in that context only sing their own songs) may be an excellent club. It may or may not be an acoustic music club. But it is not a folk club, any more than the All Wheel Drive Club is the Ramblers Association.

It is also bedevilled by territorial assumptions. What is folk music in America (or Japan, or Germany, or France) is not the folk music of England (and vice versa). It does not make either better or worse.

But it does heavily influence the answer to the question.