Try the next to get the 'AddressListMembership' with the correct value instead of null:
1. In your Exchange server, open the Exchange Admin Center(EAC).
2. Select the user mailbox affected, open properties and check the option "Hide from address lists".
3. Save the change and wait for 15 mins, then, unchecked the "Hide from address lists" option again.
4. The AddressListsMembership value should have the correct value instead of null or {}.
5. Try adding the AD object in the publication.
You can check the next MS post as reference:
==AddressListMembership and user missing from GAL==
https://social.technet.microsoft.com/Forums/en-US/d7b01252-c8e5-4558-bb61-27383139cf94/addresslistmembership-and-user-missing-from-gal?forum=exchange2010
