Answer is: yes!. Of course, it's also a matter of what degree of "what matters". I'm a little bit in the "tone freak" camp. I don't necessarily think that it is so much that the people who don't think wood is so important, is that they "can't hear", is more that "they don't know what to listen for" (because it doesn't matter(?)), and that they haven't paid attention to it, again, in their world about non essential stuff. I've paid and continue to pay very close, focused attention on these things, mostly because of extreme interest. I've gotten props for it too, on bass and guitar, both electric and acoustic (not acoustic bass). When I was younger, I was more focused on playing and becoming a real gunslinger, compliments on tone then was few and far in between. A couple of times I even got flak for my tone; I was like "Huh? Now, look at this!" babbitybabbitybiddybabing! slapping fast triplets or ripping through Donna Lee! Now, I rarely slap, and since Jaco did Donna Lee better, I don't play that anymore, other than by myself to check that I can still do it, or to show friends how crazy good Jaco was and how hard it is to pull a tune like that off, they can hear my puffs and grunts hahaha, when I play it!

Plus Jaco had that gorgeous vibrato and the little slides and vocal quality of his fretless playing, which is all the life in that tune anyway, when doing it on the bass IMO.
But comparing guitar forums to talkbass, tone is much more obsessed over, over there than here. Perhaps, it's because of the bass being more a functional instrument, no matter how you slice it, in a way, than guitar? With that being said and following this comparison with guitar and bass forums, my observation has been that: This "wood doesn't matter" don't hold much traction in the guitar world. Anyone who have spent some time with some decent examples of say, a rosewood Strat vs a maple Strat for instance, don't think that it doesn't matter. It's a very distinct difference. There are some naysayers there too, of course. But those are the types that will (and some also have) make a guitar out of cardboard, play it and say it "sounds great", or buy a Chinese knock off Les Paul, and write on forums that it's "just as good" as a Gibson Custom, so why pay $5000 extra "for nothing". I watch youtube videos of this kind, and I think "You wouldn't know good tone if it hit you in the head with a sledgehammer", about the guy talking. And the comments section is split, with people saying either "Right on, man!" or "Go rinse your ears!" It could also be some have a fetish for doing things cheap, and doing "a lot with a little", which is totally valid, but then just say so. I made a cardboard Strat, I can play music on it! I can even shred on it! Hurray! That's awesome. But don't go around claiming it's "the same thing" as a Fenden Custom Shop Strat. It's not!
To be a little serious:
I think the market pretty much speaks for itself. The fact that there is a market and support for the high end in the industry, tells me what people believe. What people do, say more about what they believe, than what they say they believe. That!, I BELIEVE!

(Oh, dear!)

The fact that Fodera is not out of business, speaks volumes, really IMO. The people who think that people buy Foderas because of "the pretty butterfly" on the headstock, must think that those customers, must be stupider than a bag of bricks. To pay that much, when "they could've" just got the same pickups, and put them in the same places on a Warmoth "whatever wood"- build, and "that would be that!", why wouldn't they do that? Perhaps there is more to it than that? Perhaps the customers are smarter, more informed, and they know exactly what they're doing? And Fodera tones are niche stuff! (Precision=The industry standard). I think people know what they're spending their money on and why; and that they're NOT fooled by bling or marketing.
I do not play a Fodera. But I do know that they just did their version of a Les Paul (I know Les Pauls very well), and their single cut is a very, very good sounding Les Paul type guitar. Great tone IMO. And it has the pretty butterfly, too!

3 words there to answer the question, and a loooooong rant! (Sorry!)

And a little Fodera love there on the end. I don't play them, but I totally get what they're about, and I do admire their work, and I'm happy that they are supported by players. (I play Fender and Sadowsky)