If I post an audio clip of me playing a guitar, you're not likely to guess what kind of guitar it is, let alone what kind of wood it's made out of. So yes, the differences in woods factor is a bit overblown.
I've read this argument over and over on this, and other, sites.
No one has ever claimed they could tell you what wood has been used in a guitar they are listening too.
Pick up two guitars that are supposed to be identical and play them unplugged.
Often they will sound subtly different, sometimes very different.
This sound has to be translated through the amp. Unless you're playing through a ton of distortion and effects, there will be a difference, albeit subtle, in the final sound that comes through your amp.
Different types of wood 'lean' towards certain properties, but that being said; even two pieces of wood from the same tree can sound different.
So, in my humble opinion; wood matters.
It may be subtle, but a harmonic there, or not there, is a difference and to say it's not is like saying all Pecorino Romano cheeses are the same.
And if you don't know what that is, your opinion means nothing to me. LOL