Personalization
It would be great if people could "personalize" their calendars. For example, some people don't have plants so they "know" they are never interested in Gartenabfall removal.
Ideally, personalization wouldn't require setting up a user account with the service. Preferences could just be encoded in URLs! But in practice it might be easier to work with accounts, if only because people are more used to that, and it is an easy solution (though maybe there are others) for switching between devices.
If we do use user accounts, it should be possible to re-use an existing third-party account (e.g. Google, Facebook, GitHub or similar). Our app doesn't need much information, mostly just an untraceable "unique identity" so that it can recognize the user even when she accesses the system from different client devices.
Google's "Firebase" services seem to be useful for this, in particular they are probably mobile-friendly because the whole Firebase thing was started for mobile if I understand correctly. Recently Google posted a story on Authenticating Users on App Engine Using Firebase. This explains how the Firebase Authentication services can be used from an App Engine application that is written in Python.