What about using Redux in React Native mobile apps? Of course, you should if you're developing the same application for the web and for native platforms. In fact, I've implemented Neckbeard News in React Native for both iOS and Android. I encourage you to download the code for this book and get this application running for both web and native mobile.
There really is no difference from how you actually use Redux in a mobile app. The only difference is in the shape of the state that's used. In other words, don't think that you can use the exact same Redux store and reducer functions in the web and native versions of your app. Think about React Native components. There's no one-size-fits-all component for many things. You have some components that are optimized for the iOS platform, while others are optimized for the Android platform. It's the same idea with Redux state. Here's what the initial state looks like for Neckbeard News ...