To answer this, all we have to do is think back to the passionate convictions on both sides during the Civil War. Both sides were absolutely convinced that they were morally right. There are still statues up all over the South, honoring "the brave men who fought for the Confederacy."
And what about the European wars of religion, the Thirty Years War, for instance? Each side was convinced that they had God's blessing, and the other side was wrong and deserved death (and worse!).
On a less bloody level, how many people living in the world today are convinced that it's morally required to observe certain religious rituals, it's morally forbidden to eat certain foods, etc.?
It might make more sense to ask, "Do ANY two people in the world share the same sense of morality?"