Complain to website owners about sites that don't work on Firefox. Try to provide detailed steps to reproduce the error, detailed error messages from the console (control meta J), and screenshots.

I think Firefox enforces some security constraints more strictly than Chrome. One error I've seen often has been blocked resources due to Cross-Origin Resource Sharing without the proper permissions, such as via Access-Control-Allow-Origin headers.

For security related errors, I emphasize that this is a potential security issue and I use FireFox for its security.