There are a few other ways in which we can style and animate React components, and they all deal with the issue in subtly different ways.
CSS modules allow you to define styles that only apply in a local context to individual elements. They look like regular CSS styles, but when they're applied to components, they are altered so that the class names given to components are unique. You can read more about CSS modules at http://glenmaddern.com/articles/css-modules.
React style is a way of creating inline styles as slightly enhanced objects. It lacks support for a few common CSS selectors, but does a good job otherwise. You can read more about it at https://github.com/js-next/react-style.