So the no viable offspring rule might not be that good for differentiating species, but that also doesn't mean that neanderthalers and us were not the same species. The more I read on it, the more I think that we were. Apparently we interbred quite a lot over the millennia.
Is there any way to tell if certain gender-pairs were more common in interspecies mating between sapiens and neanderthals? For example, are we able to tell if the male partner was more or less likely to be sapien or neanderthal?
I think that might be possible with mitochondrial dna (it always comes from the mother), but I only found 1 speculative source that draws a conclusion: "Nobody today has mitochondrial DNA like that in Neanderthals and, since it’s passed only maternally, this implies that interbreeding was more often between their men and our women." https://aeon.co/essays/what-do-we-know-about-the-lives-of-neanderthal-women
It's an essay, not a research paper, I wouldn't bet any money on this conclusion being correct.
Coincidentally just just watched this Gutsick Gibbon (primatologist) vid which touches on this a bit (though not the main topic). https://youtu.be/dy7_LousWVo