So finally I could fix it. In the end, the issue just was that the app “Bluetooth” was missing a permission to change the system settings.
You need to grant this permission to the app in this way:
- Go to “apps”.
- Enable “Show system apps” in the three dot menu.
- Look for the app named “Bluetooth”.
- Click on “advanced”.
- Enable the secret hidden permission named “Can change system settings”.
Afterwards, it just works. At least enabling. 
Anyway, it would be nice if Fairphone could fix that crash or report it to those responsible for that.
Because in such a case the app should show an error instead of crashing the whole system UI.