0) I was logged into my secondary Madden account, so I clicked "Log Out" from within the Madden Mobile game's settings icon in lower right corner of main screen.
1) Force Close Madden Mobile.
2) Wait for 10 seconds for the app to really close, then Delete Madden Mobile.
3) Open "Settings" app -> iCloud -> Turn off "Find my Phone".
4) Open "Settings" app -> iCloud -> Turn off "iCloud Drive".
5) Open "Settings" app -> iCloud -> Turn off "Backup".
6) Open "Settings" app -> Safari -> Clear History and Website Data.
7) Open "Facebook" app -> More -> Privacy Shortcuts -> More Settings -> Apps -> Logged in with Facebook -> Madden NFL Mobile -> "Remove App" -> Remove.
8 ) Repeat step 7 for any other Facebook Profiles you might have which are tied to secondary Madden NFL Mobile accounts.
9) Force Close Facebook app (and all other apps which are still open).
10) Wait maybe 10 seconds (if more apps were forced closed, wait 10 seconds per app) so it finishes closing.
11) Reboot your Device (for Apple devices, hold down the HOME and POWER BUTTON until the WHITE APPLE LOGO APPEARS).
12) Open "App Store" -> Search Madden Mobile -> Install Madden NFL Mobile.
13) Make sure Facebook App is logged into your troubled (locked out) Madden account's profile.
14) Open Madden NFL Mobile.
15) Click "Allow" when the screen asks if you want to share your facebook profile with Madden NFL Mobile.
16) Say 10 "Hail Mary's" AND PRAY THE GAME LETS YOU BACK IN!!!