Well, I’m not EA Support, but the troubleshooting steps I’m used to, may help anyway :)
If you’re using the FB app on your iPad, it may be necessary to delete that one first.
1. Force close all open apps (doubletap the home button and wipe them out 2. Log out from all online accounts
3. Clear the Safari cache (settings -> Safari -> delete history and website data)
4. Wipe out the settings
5. Restart your iPad
6. Open Safari and log in to Facebook
7. Open the game and try to log in with FB in the account manager
(Don’t forget to log out from FB in Safari at the end.)
I don’t know, whether it will help to solve your issue, but it’s worth a try.
If you still need help from Support, you can reach them in your game. Tap the three dots at the bottom right, then info, next Online Support and finally the speech bubble at the upper right at that window.