I've heard this story many times before in musician's circles. It's always been framed as either, "His harmonies were too dissonant for his time. The common ear took his piece as an insult". Or, "it was too pagan". I feel there might be more to this. Was Stravinsky an otherwise controversial figure? What was the scope of this "riot"?
I'm not sure if this will survive moderation and I can only partially answer.
1.)Rite of Spring was groundbreaking in it's departure from musical norms of the time.
2.)People disagreed about whether it was good or not and since music is both an objective and subjective experience, there was room for disagreement.
3.) Dueling factions were cheering/booing and that escalated and got out of hand.
Here is a book that gives some context that is available online. van den Toorn, Pieter C. Stravinsky and The Rite of Spring. Berkeley: University of California Press, 1987. http://ark.cdlib.org/ark:/13030/ft967nb647/