Edit: This likely is the best solution assuming you are using react-redux to maintain application state:How to refresh a react redux application when data changes on DB outside of the application
Your question does require some clarification because if you are sending data across components, then you don't need to do any of the above, you change the state of the component and react should update the view. You also need to provide more details on whether you are sending data from child component to child component or from parent component to child component or from child component to parent component so that I can point you to the appropriate stackoverflow question.
See: Send data from child to parent React
Or: How to share data between non parent-child react components?
If you are wanting to send data across two different applications,
Are you using react redux at all to maintain app state or are you using react's built in state management? If you are using react redux and redux-persist, I'd recommend applying a middleware that handles changes to state and using a server-side data store and building sync operations. Does the data need to update in realtime in your other application and is that application also another mobile application in react native? Do you anticipate users utilizing the same application across different devices? Push notifications should only be used for notifying users. The approach I would use is to use a pouch-db redux-persist adapter and sync state that way so that whether your app runs on mobile, web, etc, the state syncs across devices. If its the same data but for different users, this can still work but don't couple the reducer for the data that isn't specific for a user to the user.
See: https://github.com/rt2zz/redux-persist
Scroll to the bottom to see DB engines available for redux-persist
See: https://pouchdb.com/