Try this method, download the old version of the original app (any old version) and then login there and then download the latest mod( updated apk) and replace the old original app without deleting the old app. Just replace it when installing the modded apk. This method does not work all the time.I agree, I tried and it didn't work. Hope they add facebook login in the future. Until then playing as Guest is all I can do...
Or just root your phone so that you can loggin in Google. Or just use emulator "vmos"