I guess I'll weigh in as a biochemist who studies fungi as a profession, for their beneficial properties. "Molds" are fungi, and most fungi are filamentous, they grow out as a network of branched filaments (known as hyphae), "looking" for food. Dilute bleach (sodium hypochlorite) sounds like the best treatment from what I've heard described above, although with the potential risk of some damage to the underlying material, since bleach is a general mild oxidizer. The dilute bleach followed by a rinse approach seems prudent and will actually kill the fungi if it reaches all of the fungal material. Vinegar (the mild acid, acetic acid) is an inhibitor of many molds and killer of some, and shouldn't damage most materials by brief contact followed by a wipe. 70% denatured alcohol is an effective killer of fungi and bacteria (and viruses for that matter) but just don't use it on your shellacked Mosins since alcohol (ethanol) is a solvent for shellac. The tars used in Finnish stock treatments, that were probably derived from mild pyrolysis of wood, are full of fungal and bacterial growth inhibitors (various aldehydes, phenolics, etc.), so they are very effective in preventing biodegradation of the stocks. The various petroleum oils mentioned are probably effective mostly by keeping moisture out but also by disrupting the membranes of the fungi (killing them) to some extent.
In the more than you wanted to know category: There are literally over 100,000 species of fungi (molds). Many look white but that doesn't mean they are the same species. Different species of fungi prefer different growth substrates, and grow best at different temperatures etc. Linseed and tung oil are, as was correctly stated, vegetable oils and will attract fungi capable of using that substrate. Leather slings are composed of protein, so will attract fungi that prefer to grow on proteins. Wood stocks without a linseed/tung oil treatment are probably attracting fungi that grow on wood (cellulose and/or hemicellulose). Keeping low humidity (below 80% relative humidity) will definitely prevent further growth of most fungi and the ultraviolet rays in sunlight will kill most fungi (especially the white ones described, but not black molds) that are on the surface of the material. Sunlight will not kill the fungal filaments (hyphae) that have grown into the wood in the stocks or leather in the slings simply because the light won't penetrate below the surface.