>>Until very modern times, women were usually not even passed from one tribe or clan to another, much less all the way to another species.
We don't really know what the Neandertals did, though. For all we know they started ritually killing and eating females for some misguided notion.
And what are we talking about here---our guys and their women, or their guys and our women? Big difference, believe me, I'm a girl.
We DO know what most of us would do if one of you boys dragged a Neandertal woman back to camp, and that is: her kid would not play with our kids. (Nor mate with them.) The Neandertal who survives in our camp would likely be a woman who would not become a grandmother to anybody. If a male, he would likely not become a father to anybody.
And unless they were even stupider than we currently surmise, the Neandertals would have had similar results with a Cro-Magnon in their camp.
Since we do not find mixed communities, this would have to be the scenario:
Their guys had sex with our women who returned to our communities, bore the product of that sex, and raised it to adulthood.
Any other scenario I can think of requires a mixed community of modern humans and Neanderthals.