When I enable anonymous users, the offline app no longer shows the login page but attempts to use the anonymous session. This is not correct because the anonymous role does not have access to any navigation items in the offline profile so the app should show the login page.
Ticket: 50851
It seems my edit got lost somehow. Once again: The real app does have anonymous pages for the desktop browser, for the login widget and forgot password functionality. When I turn on anonymous access, the offline login breaks.
Edit 1-5-2017:
The LoginForm widget works offline too, just don't enable the forgot password function. The issue can be solved using the same navigation configuration as with online/hybrid.
I created a pull request on the login form widget for the offline enablement.