I was having issues too from my iOS device. The MDE app was basically frozen, sometimes it would show the login, other times I couldn't get past the "This is your new dynamic home screen" tour pages.
Similarly, I had the app before, then offloaded it, then was trying to reinstall it recently for an upcoming trip. We also had visited Disney Land in the mean time and used their app if that follows suit for anybody else. What finally worked for me was the following:
1) I deleted both the
DisneyLand app and the Disney World (MDE) app.
2) I re-installed the DisneyLand app and logged in from there first (answering yes to the location/bluetooth stuff)
3) I re-installed the MDE DisneyWorld app and was (ahem) magically able to use the app
My only guess is that the apps must share some data on the phone. Hopefully this will help you or somebody else. This worked for two devices in my family that were having the issue. We had a new iOS device that didn't have any problems. I'm not sure if the uninstalls/reinstalls are needed, or just logging into the disneyland app flavor first.
At any rate, good luck!