Here's a non-sarcastic answer that I think (I hope ?) most will agree with :
- two instruments spec'd exactly the same will probably sound different
- everything affects the resulting tone to a certain degree
- some things affect the tone more than others (pickups > pickguard material, hopefully not triggering anyone here) : maybe the finish contributes to 0.1% of the final result, in which case, does it affect the tone or not ? How significant is it ?
- "a certain degree" might really be inaudible to some and not to others, because we all hear things differently
- it is hard to definitely prove things don't affect the tone, because isolating one single factor in a man-made instrument built with different pieces of wood and different pieces of hardware located at slightly different spots, assembled differently, wired slightly differently and tested in different conditions is impossible : the instrument (and the measuring device) is a complex system where everything interacts with everything else
- it is a bit easier to prove things do affect the tone, but still hard depending on what is tested, for the same reasons (strings = easier but still tricky, because strings change alter the setup of the instrument for instance)
- I think videos of cardboard / epoxy / metal / crayons / other alternative material guitars are fun but only help to argue that the material of the body is probably not one of the main contributors to the tone (cardboard strat still sounds like a strat); it still does not prove that it does not impact it (no control)