Jazz term. A mouldy fig (or, for our American readers, a moldy fig) is a fellow who listens to and enjoys pre-bop jazz. Dixieland. Someone who’s not hip to the bop, you know? You can extend it to mean someone who's just not up on whatever is happening now. You know, "I'd send my dad the pictures, but that mouldy fig doesn't even have e-mail." Or maybe, "Call me a mouldy fig, but I prefer reading magazines to reading your goddam blog."
(mangopuddingblues.com)

What mouldy figdom... boils down to is the snooty, hipper-than-thou dismissal of anything remotely popular and/or new in music. Whatever the masses like couldn't possibly be good, and whatever's going on now was done better 30 years ago.

and as defined in a Dixieland-themed blog