So for me at least, It doesn't make sense, even if Eywa can somehow affect the evolution of organisms on Pandora over time, for all the species' neural tendrils to be interconnectable. So what I postulate is that at some point in the past, a common ancestor had a neural whip. This may have been left-over from evolving from a form similiar to the Tree of souls. This would still provide a benefit both in terms of mating and in terms of accurate communications about subjects such as food and predators. As species evolved the neural whips of each species differentiated, so that a Banshee could not achieve a bond with a direhorse, for example. Somehow, and here my theory breaks down somewhat, the Na'vi evolved a queue that was "universal"--able to bond with any other species. Obviously, for them, this was a huge evolutionary advantage in terms of mounts and things.
What do you guys think?