Turn off syncronisation of contacts in LineageOS / CyanogenMod I want to use my phone with the google calender, but I don't want to upload all my contacts from my phone to google. 

How can I achieve this?

I said in the contacts App under Settings that the App Synchronisation is off, but then I deleted some test-contacts online in Gmail and they were also deleted on my phone.

I also tried the App "Root Firewall" and forbin access to internet to the contacts app, but still, there was this sync going on.

How can I achieve this in CyanogenMod? In the standard Android 4.1 it worked fine: there was nothing synced.

Or do I need another contact app to achieve this?
In the syncronisation screen you have to turn Synchronisation on global. Only if that is on you have checkboxes next to each category inside the google account. you can uncheck the box at Contacts then.

If the global sync is OFF you don't have this option.

I think it is a bit dangerous the first time you enter that menu, because you have to be sure your internet connection is disconnected. Otherwise the first time, when all sync boxes are still ON it will start right away to sync everything before you have the chance to disable the sync-box for contacts.

If you are offline you can setup everything like you wish and then it's fine.