I wouldn't reccomend it. I have a severly autistic cousin. autistic children tend not to listen to instruction very well. I'de be afraid that the child would get hurt. Try either horse-back riding or music. They are many places where disabled children can ride and it really makes them happy and its safe. My cousin love smusic though. He connects with it very well and it helps him understand things better.
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It depends on the individual child - like neurotypical children, Autistic children are all different.
There's nothing to suggest that gymnastics is particularly good for Autistic children, if the child has difficulty with coordination then it may be challenging at first - although it may improve their balance and coordination. Gymnastics could teach a child to follow instruction, discipline, and provide routine.