How about refusing to perform in places that allow recording devices? Essentially, anyone who is recording your material without your permission is bootlegging--committing musical piracy--and can/should be asked by management to stop/leave.

If this were a Rolling Stones concert, that would be the case. Folk venues and performances are small potatoes, scale-wise, but the principle is the same. If you or a venue doesn't want to allow live recording, you or they don't have to. Hopefully your venue will back you up and enforce your wishes--just play it off like you're Mick Jagger.