Could you explain why you think the number of hybrid offspring of Neanderthals currently living prevents Neanderthals being a different species? This is like saying that if there are a large number of mules alive that donkey’s can’t be considered a different species to horses.

There is evidence that the offspring of the Neanderthal hybrids follow Haldane's Rule [1].

1. https://en.wikipedia.org/wiki/Haldane%27s_rule