I would like to disable sound and vibration for all incoming notifications. I don't mind if phone call vibration gets switched off, too. But the users volume settings for phone calls shouldn't be touched.
Thanks to the AudioManager, muting the sound of notifications is easy:
Since nobody came up with a solution, I'm going to answer my own question.
It seems that there is really no way to achieve what I wanted, at least with the latest Android versions. So I ended up doing the following ugly workaround:
I'm now muting the whole phone (incoming phone calls and notifications) via RINGER_MODE_SILENT but also listen for incoming phone calls via a BroadcastReceiver. As soon as an incoming call is detected, the RingerMode gets reverted to its previous state. This effectively leads to the functionality I wanted to achieve.
I'm, however, extremely unsatisfied with this workaround.