It's a very touchy topic for some people, so take everything I say below with whatever amount of salt suits you:
An electric guitar is a vibrating string supported by a hard material. The string vibrates in a magnetic field provided by the pickups' magnets and is converted into AC electricity through induction by the pickups' coils. That AC electronic signal is then processed by the tone controls and passed to the amplifier. Looking at this chain of events to make a sound, the items that should have a strong effect on the way the guitar sounds are, in no particular order:
- The speakers
- The amplifier
- The amount of induction in the pickups
- The amount of AC impedance in the pickups
- The amount of AC reactance in the pickups
- The tone controls
- The length of the string
- The tension of the string
- The material of which the string is made
- The hardness of the material stopping the string on each end
- The amount of yield (flexibility) in the support
- The means by which the string is excited (plucked, for example)
But virtually everything else will have a nuanced effect on the tonal qualities of the instrument. Those nuances are probably rather important to the player.
My takeaway from that, though, is that some specs are very important in determining the tone of the instrument. For example the scale length and tuning and the type of strings used. These have a very profound effect, yet we perceive it as less of an effect because the variation is small. A 25.5" Fender and a 24.75" Gibson have a ~3% difference in scale length. The differences between Ernie Ball Super Slinkies and GHS Boomers is also nuanced. Yet, to my ears, the tonal differences between those things is significant.
Next are pickups and pots. Personally, I think, again, it's a huge difference in tone. And the values are much more profound as well. You could take any two of the same model of pickup from the same manufacturer, and I'd be unsurprised if the DC resistance (indicative of the AC impedance characteristics) were within 3% of each other. Various different models on the market have significantly different numbers of winds and thickness of wire and even different grades of copper wire (also remember those silver-wound pickups that were marketed a few years ago?, or Lace alumitones, which use very very thick aluminum single winds?), and the winding techniques can vastly vary (single/double coil [sometimes triple or more]; scatterwound, straightwound; potted, aircore; even QTuners, which have the winds oriented longitudinally relative to the strings, rather than the usual transverse direction). Pots can be 1megohm down to 250kohm. Many of my guitars have no pots at all, and they sound noticeably brighter than even 1megohm pots.
Then you get down to the construction of the guitar (solid, semi-hollow, full-hollow; bolt-on, set, thru-neck; hardtail, vintage trem, floating trem; etc.), and both the effect on tone and the amount of variation are a little more subtle.
Basically, IMO, if you put tele pickups on a strat, I'd expect it to sound more like a tele than a strat. If you made a 25.5" ES-335, and put Dimarzio super distortions in it, then plugged it into a wireless and went far enough away to kill any feedback, it'd sound more like an Ibanez or a Jackson superstrat than it would like a Gibson.
I've tested this sort of thing before, and I'm not saying that wood makes no difference, because I've proven that it does through my own experiments. But it's probably the 9th or 10th thing down on the list in terms of how much variation in tone you get from the amount of variation in parts accepted for mainstream use in the trade. Probably the most interesting thing to me was the amount of tonal variation between non-identical pieces of identical-species timbers.
But this whole topic is quite the rabbit hole to go down. If you try to quantify anything using a scientific approach, there are just too many variables to isolate to get anywhere near the point where you can start answering more questions than you are raising. Plus, so many people on the internet treat this as though it were a religion vs atheism debate where either certain pieces of aged tonewoods are the magical missing piece necessary to achieve a certain tone or else the nature of the wood makes zero difference at all. And probably most people are somewhere in the middle, like me, but it's the most extreme and vocal people who shape everyone's perception about the "debate."