Then explain why some Fender Precision Basses sound different from other Fender Precision Basses. Of course the differences will be incredibly subtle but as musicians and artists we trade heavily in subtleties...they tend to mean the difference between good and great in many regards. But hey, if you don't wanna believe in wood nymphs then wood nymphs won't exist for you. Maybe I'm nuts but I want to make music on a magic instrument.
One of the biggest influences on the sound of mass produced instruments is the tolerances of the electronics. Even the best CTS pots have a tolerance range of +/-10%, many pots are much worse than that (which is why I specified mass produced instruments, where parts with wider tolerances are going to be common place).
I'm not saying the wood has no effect. I've swapped one wiring rig and pickups from my SG to my Les Paul. They are setup the same, they are both set neck guitars, have the same strings. The only significant variable being the type and amount of wood on the guitar. While they had some tonal similarities, that is far from being the same.