For example, if you ever find yourself in Yemen and you meet a child bride who wants out, whom does your "strong moral code" compel you to side with? Do you side with her because your strong, but American moral code demands that you protect children and respect females? Or do you side with her fiance because you respect Yemeni culture?
The difference between a moral relativist and a moral absolutist is the mythological belief that there is some universal truth behind their moral code. You don't need universal truth to have a moral code.
I have a moral code (which is very similar to that of everyone who lives in a modern Western cultural context) that will compel me to act in situations that I feel strongly about. I would feel strongly compelled to stop a rape or murder (assuming I had the ability) even if it was morally sanctioned in whatever context I found myself in.
In cases where a culture is functional but but awkward, I would feel obligated to not interfere. I am very uncomfortable with the US using morality as a justification for military domination of other cultures.
Sure... these two things sometimes contradict each other.
The point being that I can live and act according to a moral code without believing that everyone is bound by the same code.