If you have configured Firefox to “Delete cookies and site data when Firefox is closed” then you will have to add their domains to the list of exceptions for it to work.
The reason is that apps using the identity service seem to do that via a ServiceWorker, which Firefox won’t allow if you set the above setting.
I was just able to fix this on my machine and thought I’d share. Finally I don’t have to use Chrome anymore for accessing the NNS. Have a good day