Fealist to the extent I find social login only is the best solution. There is a extension called "social login only" (I could not share link at the moment replying you from mobile) .
I'm just hiding the signup button using CSS, I've set that CSS code before the extension was made. Now you can simply use the new extension. But it makes everyone to login social login only.
There is a another extension called "white list domain only" by Clark , I've not tested it since my requirement already fulfilled.
Just go to my flarum profile > discussions > you will find a discussion related to hide signup button, a code to hide CSS fields code. You need to put it in appearance > CSS/less code are in flarums admin panel.
Hope that helps.