The solution going forward to allow inclusion should be shows labeled as "autism friendly" or more generally "family friendly", where productions make an effort to use less special effects, lower the volume a tad, and reduce harsh lighting (no strobe lights, no sudden bright lights, no periods of total darkness).
As it stands, though, I sympathize more with the audience than the mother and child. The audience shouldn't react harshly, and it's hard to judge how they reacted without being there, but the amount of money collectively spent to attend that show was in the realm of $125,000. It's not reasonable to ruin the experiences of other theatergoers paying that much by taking a child who has documented issues with expected elements of the show. If they do go, they should sit in the back of a section and immediately exit to the lobby if there's an issue. This doesn't just go for children with autism; any parents with children unable to behave through a show should respect the hundreds of other theatergoers and leave their kids at home.
BROADWAY: The Cripple of Inishmaan, This is Our Youth, If/Then, Hedwig and the Angry Inch (x3), Cabaret (x2), The Real Thing, A Gentleman's Guide to Love and Murder, Chicago, Les Miserables (x2) Disgraced, Finding Neverland, On the Twentieth Century, Wolf Hall Part I, On the Town, Fun Home; TOURING: Jekyll and Hyde, The Book of Mormon; LOCAL: The Twilight Zone, Anne Boleyn, Death and the Maiden, The Lying Kind, Chorus Line, Stupid F**king Bird