There are a few half-finished and seemingly abandoned ports to linux. React-native for Windows/macOS is being developed by Microsoft to support their Office teams (afaik, some screens in Office for mobile are react-native, and they want to use it on the real desktop version as well). Unfortunately since Office isn't available for linux, Microsoft isn't doing a port as well.
A fallback option for Linux could be to render the React Native app to HTML/CSS/JS using react-native-web, then package it in an Electron app. Depending on the level of native integration this could be tricky though.