To fix this by the way, just install the Facebook Container in Firefox. Somebody else (presumably a Mozilla employee?) does the extensive curation needed to get this to work and stay working. You are logged into Facebook inside the Container, but everything else is pristine, on the outside of the Container you can log into whatever and it's not connected back to Facebook.

Firefox's Container system is a powerful solution to this general problem, but normally you need to do curation work proportional to the effort being taken to track you. Their Facebook Container though comes with that curation done.

If you use Login with Facebook (you want Privacy, but you choose to Login with Facebook? Maybe reconsider your life choices) the Container puts everything you logged into this way inside the Container too, so that dissolves your privacy but you chose to have it happen.