React Native + React (for web) seed project

You can give a try to React-Native-Web, but imho you should create 2 different projects, isolate and copy what can be used on both (like api requests and util functions). Your code will be easier to debug and maintain.

Jonathan Kaufman has a good article on how to set this up: http://jkaufman.io/react-web-native-codesharing/

The basic strategy is to have a different entry point (index.js) for each platform (android/ios/web). Then the majority of your non-rendering code can live in a shared app or common folder. You'll still need to segregate your rendering code (i.e. uses of View, div, etc.), though, as that will differ by platform.

Pay attention to the comments on that article as well, as there's some good discussion on the pitfalls of this approach. Example:

By sharing a common package.json between native and web, you've glued them together by their common dependencies, the most important one being react. Let's say you upgrade to a version of react-native that depends on >= react@16, but your web app depends on some other library which depends on =< react@15. --timtas