I have managed to install F-Droid on an Android phone with the following Family Link settings:
Controls on Google Play:
- Require approval for No approval required
- Allow Up To Allow all, including unrated
Then in the device settings:
- Apps from unknown sources enabled
I have also enabled Developer Options but I am not sure if that is needed.
The source where f-droid will be installed has to be enabled as trusted but this is a standard thing.
After this the settings can be made more restrictive.