Fix "android.process.acore keeps stopping" when the contacts provider can't load it's db
I posted this question trying to find a solution for about an hour and just 10 minutes later I finally found it myself.

Going into the adb shell and running

pm clear com.android.providers.contacts


does not require root privileges and clears the cache, which seems to include the *.db-shm file.

I'm keeping this question here for future reference

EDIT: This was a misinformation. After further inspection I found out that, pm clear does in fact clear all app data, so don't run it if you only want to clear an app's cache. That command is essentially the same as clicking on the Clear Data button in the app preferences.

The reason why this worked out for me is, that the contacts themselves are stored separately. The com.android.providers.contacts package loads the contacts from that other place and provides it to other apps and therefore is called contacts provider. 

The data in the provider's db seems to only be things like the call log and the contacts you recently shared something with. Deleting this data is totally fine and fixes the issue.