To remove your Facebook Login from your LeagueRepublic account, the first step is to create a username and password to use instead:
sign in to LeagueRepublic with Facebook Login
once logged in, click on My Account
click on Settings
click on the tab LR login
enter a username and password of your choice
then sign out
Then to remove Facebook Login from your LeagueRepublic account:
sign in again using this username and password instead of your Facebook Login
go to My Account
click on Settings
click on the tab Unlink Facebook
click the button Unlink
you'll no longer be able to sign in using the Facebook Login button