Just tell them you're not stuck in the past but you respect it. Tell them they need to fit the venue, not the other way around, and that's a fact of life. They can complain about the unfairness of life (and booking) as much as they want, but no matter how much they want the gig, it won't make their potential audience want to hear them any more.

They might be playing the 'folk' of tomorrow, but somehow I doubt it. That will be the gems of songs that people will want to sing and pass on. It doesn't matter one bit anyway, because the bottom line is that you're always right when it's your gig, your audience, whose tastes you know, and your decision to book them.