I'm using firebase in my android app and facebook SDK for logging-in as well.
The only problem I'm facing is that when I log-in with facebook, then log-out, the facebook login button is in the "log-out" state and when I click it, it asks if I want to log-out.
What I do to log-out:
You have to log out from the Facebook SDK too, using the LoginManager class (com.facebook.login.LoginManager).
These two lines work for me:
Hope this helps :)