@popeye1945,
Here is my practical example... please show me how this will work.
The White colonizing culture believes only monogamy is moral and child brides are immoral. The indigenous culture believes that polygamy is moral and preferable and that giving away adolescent girls is the best way to ensure the benefit of their "common biology".
The facts are
1) Most indigenous cultures have polygamy.
2) Many of the animal species closest to humans practice polygamy by nature.
3) There are good biological reasons that polygamy ensures the strength of genes and the welfare of communities (in humans and other animals).
We know what happened in history. In North America, in Australia and in other places White colonizers met the indigenous cultures and said "we are going to stamp out polygamy". The indigenous cultures said "No you aren't". Then the White colonizers stamped out these practices by force (with different degrees of success... polygamy is still practiced in aboriginal communities in Australia).
The only way to get to the "common morality" you are suggesting is by the dominant culture imposing their moral values by economic or military force. This has happened time and time again.
If an indigenous culture came to you to tell you, we don't accept monogamy and you must change your culture to accept the morality of polygamy, how would you react?
Global morality always means the dominant culture imposing its will on indigenous cultures. It is never the other way around.