Based on my research and this question it seems that some WebSocket based Nodejs libraries do not work with React Native (e.g. Paho's JS library for MQTT), but others do work (e.g. SocketIO and Firebase).

Is there any way to know other than trial and error which ones are likely to work?

Summary:

Sounds like most WebSocket based libraries should work and that inconsistencies with the way React Native implements XMLHttpRequest is not an issue.