In Auel’s defense, much of how she described Neanderthals was speculative at the time because so little was known about them. There was no DNA analysis; the hyoid bone (as Colibri pointed out) had not been discovered, and its shape would determine whether Neanderthals were capable of articulate speech. What we knew at the time was that Neanderthals had a larger brain capacity than us, a larger occipital lobe, had the same injury rate as rodeo clowns, left behind no evidence of art, died younger than Cro-Magnon, and stopped showing up in the fossil record shortly after Cro-Magnon appeared.
What we know now, thanks to DNA analysis, that there must have been interbreeding, because anywhere from 1-4% of non-African Cro-Magnon DNA derives from the Neanderthal genome. We know that at least some Neanderthal were pale, freckled, and even had red hair - a different genetic mutation from what created red hair in Cro-Magnon DNA. Now that a hyoid bone has been recovered and found to be virtually identical to our own, paleontologists make language the default assumption. They also have the same copy of one of the genes we know contributes to speech in humans. They may have made jewelry and marked their belongings for some aesthetic reason, they very likely marked their bodies with ochre and manganese, and they probably did build permanent shelters out of mammoth skulls.
Using gestures for communications? Completely believable. After all, bonobos and gorillas do it.
Possessing language skills? Well, Neanderthals had enough space in their skulls to put abstract thought into an externalized form. Not a wild grab.
A language completely based on gesture? Erm, a lot less plausible, but understandable given Auel’s needs for a story that wasn’t going to turn into Ayla of the slightly-more-evolved-than-apes Neanderthal.
Racial memory? Total and complete bupkus, especially if you stop to consider that if it were even plausible, the memories transmitted could only go up to the moment of the next zygote’s conception.
I don’t believe her depiction of Neanderthals as dark haired and dark eyed is necessarily racist. After all, the Inuit live above the Arctic circle, and they’re entirely dark haired and dark eyed. Yes, inevitably a population will select towards less expression of melanin in a polar region, but that means light brown eyes, not blue eyes. Blue eyes require a specific, random genetic mutation. That mutation isn’t inevitable, and it doesn’t show up in Cro-Magnon until 18,000 years ago. There’s no current evidence that the mutation ever occurred in Neanderthals.
All that being said, everything after the third book is crap.