When I read discussions about morals they inevitably get to the issue of relativity vs absolutism. A person arguing for relativity of morals, from my understanding, is arguing that morals are not held constant through differing groups, but instead are relevant to that culture, meaning certain things may be viewed as morally different from those of another group or culture.
What also gets implied, although I'm not sure if this is true, and seems to be a personal conclusion drawn from the concept of relativity, is that due to the differing context of how morals may be formed, if one moral rule seems at odds with that of another culture, that a person from another culture has no right to judge the validity or lack thereof of said moral rule in question. This implication is usually snuck into the conversation, and it may be held by a proponent of moral relativism, however it is not actually part of what moral relativism seeks to explain.
Furthermore, there also seems to be a misconception that a moral relativist does not believe there to be any universal moral rules. I hold this contention to be false, as due to the fact that groups of humans require a certain harmony in order to thrive, there will almost always be certain behaviours which are off limits, such as murder, rape, stealing. These, I advocate, are moral universals, which tend to arise in a human system of morality due to the dynamics of a group.
Therefore a moral relativist can still hold that certain moral rules are generally right and not be seen as immoral. Furthermore, a moral relativist might contend that we have no right to judge what is right or wrong in another culture, and still have a solid system of morality which was instilled in them. Morals tend to operate at an emotional level, therefore we might hold that we have no right to judge another cultures morals, and still have an opposing emotional reaction to that culture based on our own morals.
The issue of morals is a complex one, and one that I think needs more fleshing out as it seems there are many layers which tend to get confused during discussions.