I first encountered this idea through RDOS. At first, it seemed repugnant to me. Then I started reading about Neanderthal and wondering about them. We do know some things about them that are fairly certain. That they lived in small groups of 10 to 15 people, occupying the same campsites for many generations. There is no evidence of long distance trade and only a little of short distance trade. Genetic survival requires a group of about 250 reproductive individuals, and they survived for at least 250,000 years, so they must have mixed it up with their neighbors a bit.
The main meat that appears in their diet is reindeer. These are relatively small animals, easier to hunt than mammoths, which I suspect they mostly scavenged for their giant bones, as there is evidence of Neanderthal shelters built of mammoth bones. There is evidence that they made use of trap pits for catching prey, and this would also have made hunting easier in small groups and maybe explains why the women seem also to have been hunters. There is much evidence that they cared for the old and sick. Their survival no doubt depended on compassion to others in the group. In such a small group, everyone counted.
Other evidence seems strong that they had to have made tight fitting clothes. They are probably the inventers of clothing, as it would not have been needed in Tropical Africa. There is also evidence that they must have stored food for winter in order to have survived. They developed a complex procedure for extracting pitch from birch trees for hafting spear tips, so they had the capacity for complex thought and action.
The reason it makes sense to me that it is connected to autism is that to live and survive in Ice Age Europe for so long, they must have had to be very adapted to long periods inside a shelter waiting for spring and hunting season. It would have been a perfect selection environment for quiet, inward, self-occupied people with low social needs. It seems to me that flexible sexuality and a tendency to asexuality would also be adaptive: Having a baby in the wrong season in Ice Age Europe may well have been fatal for mother and child.
Their DNA appears to be wide spread in non-Sub Saharan African people, so clearly there was interbreeding and some adaptive advantage to Neanderthal genes. Considering that many autistics are very clever at problem solving that involves huge amounts of solitary thought and experiment, as well as having very low social needs, it seems like Neanderthal genetics could have something to do with it. RDOS's examination of the evidence seems to support the hypothesis as well as results here so far.