Generally this works just fine if the console you are using is set to your “home console”. That’s what the home console toggle is for. I could see this being an issue if you have multiple consoles in your house, or you are game sharing with another profile.
I started using librewolf about a month ago but I’ve (unfortunately) switched back to Firefox because of multiple compatibility issues.
Edit: I should add that I switched from Firefox to Fennec (a fork of Firefox) on my phone and that has been working fine.