Who says that a society's moral values don't have causes? The issue is whether those causes are historically contingent (colloquailly, whether history could have happened in a way that different moral positions were adopted in a particular time and place).

Alternatively, can I suggest you taboo the word justification? The way I understand the term, saying moral positions are justified is contradicted by the proliferation of contradictory moral positions throughout time. (But I'm out of the mainstream in this community because I'm a moral anti-realist)