Given the diversity of human characteristics (short dark African Pygmy; blond blue-eyed Scandinavian; Japanese; etc) it makes more sense to consider Neanderthals a different race of humans rather than a different species, given evidence of interbreeding.
Agreed, up to a point.
This entire thread is premised on the idea that interbreeding between humans and Neanderthals can be, and has been, demonstrated through genetic markers.
For sake of discussion I accept the premise, even though am not at all certain it has been proved beyond reasonable doubt. No doubt that future research will either confirm and reconfirm it, or possibly just show how today's researchers got it wrong.
In either case, that would not be the first time it's happened. ;-)