I teach archery to kids for our club, and we have had several kids with autism come to our classes. We may have had more than I know about, but several where the parents have volunteered that information up front. The class is an introductory class, but some of the kids like it enough to take the class more than once. Some of the kids with autism have taken the class 3 or more times, probably the most repeat visits of anyone. Depending on the type of autism, kids can be unpredictable and need to be watched a little more closely, but then, we make a point of watching all the kids closely anyway. All the kids we have had with autism have been able to communicate with us and respond appropriately to the things we are doing and saying, so I guess they're not very far up the autism scale.
My experience is that any kids, autistic or not, respond best to archery instruction at 8 years old or older. There are exceptions, of course; Mozart was supposed to have written a symphony at 3, but that is my experience with average kids.