I think most societies are morally absolute. Relatively few accept the "that's your truth/morality, you can't impose that on me!". This doesn't imply that all morally absolute societies have the same mores.

Nearly every society I look at has a widely diverse set of morals present in it. You might get widespread agreement that "rape is bad" but when you start to look closer there is disagreement within that about what constitutes rape (something I don't understand personally, but I can't ignore that it exists).

There is widespread disagreement about the use of force, who should care for the sick and poor and when, and so many other things.

So maybe I don't understand what you mean by a morally absolute society.

I don't understand your point of "that's your truth, you can't impose that on me." That's literally how most of us have to get along. If we were unable to accept moral differences in other people, we would be completely unable to function as a society. I don't believe there has ever been two people who have completely agreed on what's moral or not.