I can't suggest anything, I'm afraid—I haven't worked with Windows and Linux targets using React Native. But it appears that there are React Native rendering targets for Windows and Linux (https://github.com/Microsoft/react-native-windows and https://github.com/status-im/react-native-desktop). I'd probably start by looking there.

And of course, because React Native can build to web, one could ship Electron apps for platforms with lower priority for your business.