I've also experienced mold in my keggerator. Not in a basement, but inside an airconditioned home (in FL). I started using a defumidifer granules/powder that I picked up at Home Depot. Been awhile since I used it as my freezer eventually died & haven't replaced it. I would still occasionally pull everything out of it & clean it up.
Another humidty caused issue besides mold is rust. I've seen freezer keggerators start to rust - starting with scratches, and progressing as rust is wont to do. If you see any rust starting, clean it up & paint with enamel appliance paint.