Popp's fiddles don't use shouldComponentUpdate, as far as I can tell. They replace using props (application state) by components-local state and an animation prop. I'm not entirely certain that his semantics map to the original ones (in terms of expectations).
My bad :x JSFiddle is unusable on mobile and I assumed it was using shouldComponentUpdate. Anyway, the conclusion still holds, you can refactor your code to be performant while keeping in the React paradigm.
You have a lot less control over the performance of your app with data binding.
