Update: I got it to animate all of the divs. My mistake was that I had the divs changing their position in the DOM, in addition to changing the CSS properties. Some of the divs didn’t change position in the DOM because their index was the same both alphabetically and by population, and these were animated.
I played with React some more, this time loading it from a CDN with the jsx compiler. I set the CSS properties on the divs and tried animating them using CSS3 transitions. Some are animated while some move to their new position instantaneously.