Any privacy effort is laudable. Then again, if you're serious about protecting your users' data and privacy, Facebook login is the elephant in the room.
I use authentication services like auth0 and AWS cognito. The first one I think is completely safe for privacy, the second one is used for convenience (I think the service is good for stuff you host on AWS anyway, although it is generic, so it isn't restricted to that).
But using an auth-service is mostly about deferring risk of breaches to people more proficient in security. That comes with the cost that said auth service can know which services registered users are using.
The author is correct though. While a user that employs such an auth service, it can be good practice to hash the mail-address or even other identifiers for you own DB (you still need that to associate state with a user).
I don't have a FB account fwiw.
Though I don't know about it being compliant I suppose Facebook Login (and other forms of SSO) shifts the reliability to Facebook.