I think there's way too many differences between dwarves and neandertals to use them as models. Neandertals are practically human; hell they have "human" in their genus name they probably interbred with us. Dwarves are definitely further off...maybe still in the same genus, but it'd be pushing it. In any case, if there were a significant advantage to them all having beards, I don't think growing hair on your face when you've already got it on lots of other body parts is something that would take so long to evolve. It's certainly not an eye.
Of course, all these rambly evolutionary arguments are still influenced by the fact that I'm a strong ladybeard partisan.
Also, between the androgynous nature of dwarves in DF, and having read Discworld at a young age, I have enough reason to support beards, but that picture of the crossbow-mom pretty much clinches it. And is probably a sufficient cause in itself.
Edit: Actually, dwarves would probably be in the same genus, as they're also as intelligent as humans. Then again, they're probably intelligent in a different way - I think the way their minds work would be, while similar in some ways, fundamentally alien in other ways. The question is, if a less-intelligent creature like Homo Habilis is closer to us than an equally but differently intelligent creature like a dwarf? If not, dwarves would be "homo beardmagmus" or what have you.