Non-removable MDM profiles cannot officially removed without doing a full system wipe. This is a problem when you restore a system from Time Machine after you enrolled it into the MDM, as the MDM will break, leaving you unable to re-enroll the machine.

Here's how to remove a non-removable MDM profile:

1. Boot the Mac into Recovery Mode (hold down command+R during startup).

2. Go to the Utilities menu and open Terminal and type: crutil disable. This will disable SIP (System Integrity Protection).

3. Reboot into the OS.

4. Open the integrated terminal and type:

cd /var/db/ConfigurationProfiles 

rm -rf *

mkdir Settings

touch Settings/.profilesAreInstalled

5. Reboot.

6. Boot the Mac into Recovery Mode (hold down command+R during startup).

7. Go to the Utilities menu and open Terminal and type: crutil enable. This will re-enable SIP.

8. Reboot into the oS.

The profile will be now removed and you will be able to re-enroll the Mac to your MDM.