Samsung just replaced my Galaxy S4 for me yesterday nd I have been unable to sync FB contacts to the phone contacts. AT first the login to the Galaxy 'app' within facebook would fail, I discovered i needed to updat ethe Samsung SNS app. I did this. Now I can login, it syncs calendar and photos but NOT contacts.
I have uninstalled FB app and Messenger app and reinstalled etc. Nothing is working. WHen I first try to set up account sync through the phone settings, it only shows calendar and gallery sync. I have to go into COntacts > Settings> Accounts > Facebook to get it to show 'sync contacts'option. I hit sync, and it takes half a second to say 'Last synced at Date/time'. Unsurprisingly it hasnt actually synced!
Like the OP, when I go into the app (which I remember in previous situations as the 'fix' for this problem) there is NO sync contacts option under app settings.
WTAF FB????? Please help, its driving me crazy.