Well, "irrelevant" is in the ears and feel of the musician. This is why "does tonewood make a difference" and "does tonewood matter" are two completely different questions in spite of the efforts of many here to say they are the same question. For example the wood in my Squier P-bass is not alder and should be. Admittedly the difference is slight, but it matters to me.
If wood selection matters to any one person, then it matters, period. How much it matters, why it matters and who it matters to is irrelevant, at that point people are just arguing about shades of gray and preferences. I don't think anyone can argue that there isn't a person on the face of the earth that gives a hoot about what wood their bass is made from. As long as one person cares about their wood selection then we can't claim it doesn't matter. We can only claim it doesn't matter to us.
It's kind of like a car with either an automatic or manual transmission. There have been cars made that perform equally well in either transmission type. I have no problems driving either and really have no preference, to me it doesn't matter. But it would be foolish of me to say transmission types don't matter when buying a car. To some people they matter very much, even to the point of it being a deal breaker, therefore it matters. It's that way for me on P basses. If it's not alder I'm not interested - it matters.