Children not clapping did happen too, (and some were even expected to have hissed, which was later written into the 1928 playscript and 1911 novel). But my all time favourite anecdote about it is from Pauline Chase (who played Peter)'s intro to Peter Pan's Post Bag 1909:
Children love to clap their hands at the play because then they feel that they are really part of it, and you can see them holding their hands poised ready to seize an opportunity. Their great chance is when I ask them to clap their hands if they believe in fairies, and so save Tink's life. But they are very wrathful if any one claps who has the reputation of being a cynic, and once there was quite an uproar in the front row of the dress circle because of a girl who clapped. Those about her pulled down her arms angrily. "How dare you clap," they cried, "when you know you don't believe in fairies!"
There was one dreadfully hard-hearted little boy who came to the theatre not to clap. That was his object for coming, and he came round "behind" to tell me so in the middle of the play. His teeth were firm set. "I won't clap," he said doggedly; "I'm not going to clap." And when the time came he didn't clap; above the clapping of all the others I could hear him shouting from a box, "Peter, I'm not clapping."