Wipe off the mold with a damp rag. If it's really bad, use a small amount of bleach in the water. Let it dry thoroughly.
Apply BLO to the entire stock and rub it in. Let it dry.
It is relatively dry here and I still get mold on my stocks in storage. The key is maintenance. I don't believe you will ever get rid of the mold completely once it gets into the wood. Mine probably got contaminated while in storage at the CMP.
Don't let them cross-contaminate each other. Don't let the fungus eat your leather slings, either.
Use a Golden Rod heater inside your gun safe. They lower the relative humidity.
If it were really, really bad, something that was not controllable with regular maintenance, you could try a fungicide from the gardening center.
You could try a UV LED flashlight. There are safety issues for your eyes but those are easy to deal with (use the safety glasses).