I see. One can click on a particular day (anywhere in "day rectangle") and then switch to the preferred view via the keyboard shortcut. This is particularly useful if one wants to use "week view" (see also my answer which is for "day view").

Thank you, shrinking the font size also helps! Switching to the day or week view does not always work since the calendar remembers the last day view.

@eyal83 Unfortunately yes, you have to quit and restart FaceTime.

After playing around it seems to work now. Turning it off and on seems to fix it. However you have to wait a little longer until it goes to sleep (in case it is charging).

In my case it was the Screen Sharing option which I had to turn off. It seems like you have to disable all options in System Preferences -> Sharing.

@MarcelStör I'm on macOS 10.14.6 and the window does not disappear if I turn on "do not disturb". (I tried turning it on/off before and also during the call)

@MarcelStör Thank you very much! I will try it out and update my answer accordingly.