The biological definition of species includes reproductive isolation. Two different species mean normally some kind of reproductive barriers. In this sense, if two diverging groups of animals X and Y mate and the offspring is fertile they are still in the same species and will split sometime in the future. How we define the splitting time is the problem. Neanderthals and sapiens are only partially fertile, so by definition were two different species that diluted into one. Red hair and green eyes are consider Neanderthal contributions. Modern sapiens is clearly an hybrid.

But the field has gained a lot of complexity in the last decades. There are ring species, and cryptic species, and sometimes the DNA of a parent is entirely discarded. Changing our point of view is possible with better data, except that we need to find this data first.