Does natural {peanut, cashew, almond} butter require refrigeration?
I don't think I've ever seen peanut butter grow mold, natural or commercial, refrigerated or not. What will happen with natural peanut butter is that the fat (of which there's plenty) will go rancid over time.

The oxidation process that leads to rancidity requires heat, light, and usually oxygen; keeping it in the refrigerator will therefore slow the process down significantly.

Manufacturers are probably not required to put the "keep refrigerated" warning on nut butters because eating rancid food technically won't kill you or make you seriously ill. When a product says to keep refrigerated, sometimes that's for safety, sometimes it's just for quality - in the case of peanut butter it's typically the latter.

Commercial peanut butter has a ton of sugar and other preservatives, which is why refrigeration is not necessary, even for quality purposes.