I recently unpacked a container of furniture that had been sitting on a dock for way too long in a humid climate, and yes it was really moldy.  I  sure would appreciate any tips you might have for cleaning the mildew stains without ruining the natural color of the wood.  Some of it has an oil finish although some is finished with polyurethane and an older piece looks like it has a shellac finish.  Woods include cherry, walnut and mahogany.

I have cleaned it with a mild antibacterial soap solution, and then wiped down with a 10% bleach solution, leaving it for about 10 minutes, but some of the mildew stains are more stubborn than that.

Thanks in  advance for any help