A low level diversity will not help us much with this argument. Suppose, for example, one culture considers marrying a second cousin to be morally wrong while another culture does not. This sort of diversity is compatible with a more fundamental agreement. 

Perhaps the people in these different cultures are applying the same fundamental principle to different circumstances. If there is a fundamental agreement of this sort, the argument fails to establish anything important.

In order to get beyond this problem, I think we should assume for our purposes that there are fundamental differences of moral principle between some cultures.