I suspect they wouldn't be integrated and perhaps even be persecuted like we do to those who have a different skin color or funny accent. Perhaps we might even see movements like Neanderthal Lives Matter.
There was a science fiction story/series in the '90s that addressed this issue. Neanderthals (derogatorily called "slopes" because of their foreheads) were considered sub-human and widely employed as slaves. The story was pretty brutal, I couldn't make it all the way through. Tried to find the name of the story/series/author for this thread, but my Google-fu was insufficient.