When I first heard about React Native, I automatically thought that it would be some cross-platform solution that lets you write a single React application that will run natively on any device. Do yourself a favor and get out of this mindset before you start working with React Native. iOS and Android are different on many fundamental levels. Even their user experience philosophies are different, so trying to write a single app that runs on both platforms is categorically misguided.
Besides, this is not the goal of React Native. The goal is React components everywhere, not write once run anywhere. In some cases, you'll want your app to take advantage of an iOS-specific widget or an Android-specific widget. This provides a better user experience for that particular platform and should trump the portability of a component library.
Having said that, there are...