Interbreeding not inbreeding.
In other words they bred with the other humans that immigrated into Europe.
But there were a lot less Natives then immigrants. So the end result was like a drop of ink in a gallon of milk. They were diluted and spread out.
The fact that a male Neanderthal/female Cro-Magnon would have probably resulted in the female and probably baby dying while male Cro-Magnon/female Neanderthal would have resulted in a live birth and live female would not help to keep the Neanderthal culture alive.
Thanks for info. Interesting
Male Neanderthal culture would have primarily been about hunting and killing. Female Neanderthal culture, like female Cro-Magnon culture would have been about making clothing, preparing and storing food, containers, child rearing, tending fires, etc. Which is more important for defining civilization? There are so many aspects of culture that we have no information on regarding who invented it and when, but I’ll bet a lot of it was done by women.