Here’s my solution to the problems inherent in moral relativism (i.e. problems like if it’s OK for one person to murder another in someone’s eyes, then we have no right to stop him/her). I think moral relativism ought to be viewed as one axis of a two dimensional paradigm. So this one axis might be labeled “X is totally acceptable” and “X is totally unacceptable” at the two ends. On the other axis of this two dimensional paradigm, we have the labels “X is culturally taught” and “X is genetically hard wired”. So for example, the Jewish maxim to respect the sacredness of the Sabbath is clearly a culturally established moral principle. It falls on the extreme end of “X is culturally taught”. But there is another Jewish maxim that says “Though shalt not kill” - this, I think, belongs on the other end: “X is genetically hard wired”. It is my belief that human beings, by and large, have a strong deeply imbedded instinct not to kill another human being, and therefore can be said to be genetically hard wired. This is not to say that it cannot be overridden, but it requires careful psychological programming (such as military or law enforcement training) or exceptional circumstances (self-defense in life-or-death situations). Neither is this to say that such instincts are equally effective in all human beings - there are a few sociopaths out there. But on average and under normal circumstances, the human tendency is to avoid murdering other human beings even if it means enduring great hardship (extreme anger, desperate situations, etc.). I think this is the case regardless of the cultural background from which an arbitrarily chosen human being is taken.
There are other examples of instinctually rooted tendencies and inclinations that I believe to be common across various cultures, such as the tendency to respect and care for children, the tendency not to want to hurt another human being, the tendency to seek one’s own happiness and wellbeing, the tendency to respect other’s sexual rights, the tendency towards honesty and truth telling, etc. I say again that the great majority of these can be overridden by cultural programming, some of them very easily, but it is not the difficulty with which one can subdue these moral inclination on which my argument rests - rather it is a question of the source: does it stem from what we have been taught or will an individual, left to his/her devices, develop and grow to follow these inclination naturally. If it is natural, I say that falls on the “X is genetically hard wired” end. If it falls on this end, then I say we ought to take a more absolutist view of its moral standing.
Now, when I say “absolutist”, I don’t mean that such moral principles have an independent existence from human consciousness and human life - just that it doesn’t vary, at least not by much, from one human being to another (cultural influences notwithstanding). A key point to keep in mind, therefore, is that there are hypothetical scenarios that one might imagine for which this absolutist view might have to be retracted in favor of a relativistic view once again - even for the whole of humanity. For example, what if we were visited by an alien race whose neural wiring was so drastically different from human neural wiring, resulting in their upholding of drastically different moral values, that we had no choice but to fall back on relativism to resolve the conflicts between the values held by each species (at least philosophically)? So the absolutist end of the spectrum certainly isn’t a lower limit, it’s just a limit insofar as those concerned are human beings.
I say the absolutist end of the spectrum ought to take precedence over the relativist end, not so much because this brand of absolutist sanctions moral principles belonging to that end as absolutely “correct”, but that there should be very little difference between where one human being stands on such morals compared to another (again, cultural influence notwithstanding). If we take that approach, I think a lot of the problems inherent in moral relativism can be resolved. This is more of a practical solution than a principled one (i.e. it answers the question of what we ought to do given the moral conflicts stemming from relativism rather than the question of are such moral principles true), but I’ve always thought practical solution are more important than principled ones.