Just to confirm, is your email address set as public or private on Facebook? This could've caused this issue.
Let's try making the email address public and head to your Facebook Settings > App, and remove Spotify from it. Once it's removed, head to the Spotify app and click the blue "Log in with Facebook" button, you should have a pop-up to authorize Spotify again.
Let me know how it goes.
“Music acts like a magic key, to which the most tightly closed heart opens.” ― Maria Augusta von Trapp