I think this thread is mistitled.
The folk club in question is in no position to dictate what's traditional and what isn't (and evidently isn't competent to make that judgement anyway), and there's no point in making an effort to comply with their mysterious code. Not even if you are desperate for a booking at that club. I'd guess that "not trad enough", or "too trad" or any other excuse the club organiser makes really means either "not good enough" (I'm not suggesting this applies to Faye + friend) or much more likely "not famous enough". No point in arguing about it, just look for gigs elsewhere - they will happen! "de gustibus non disputandum"1
As for your choice of material and style, do what works best for you and what you believe in. In the end that's what will work best because it will generate energy and enthusiasm that you can communicate to an audience. I've seen someone trying for a gig at a club, singing material that he evidently wasn't comfortable with because it was what he thought it was in keeping with the club's booking policy. It didn't work; sticking to what he knew best might actually have worked better.
Anahata
1"there's no accounting for taste"