Is Morality relative to a culture? Professional moral philosophers who are relativists through and through are an extremely rare species today. It may be there in good numbers in other academic departments, but not so in Philosophy departments. One of the reasons why professional moral philosophers who have thought through on this subject do not take such a view on morality is that moral relativism leads to an unlivable society.
'How do I lead a good life?' or 'What is the right conduct?' are the kind of questions that bother moral philosophers. This is so because these are the sorts of questions that any rational individual would seek or ought to seek; they are also the concerns of any given society. Every moral theory aims to seek a flourishing society, not just a flourishing life of an individual. Given that moral theory aims to seek a flourishing society, if a moral theory leads to total breakdown of a society or its logical outcome would lead to a breakdown of society, then it has to be rejected.
Take the case of lying. Is it okay to tell a lie? No way. Why? If lying is okay, and everybody begins to tell a lie at their own liking and there is no moral prohibition for lying, how would a society look like? That kind of a society cannot function. Let me explain why it is going to be the case. If A tells me a lie again and again and again, and I tell a lie again and again and again to B, and B lies again and again and again to C, how on earth will there be meaningful communication between four of us! And without meaningful communication, a society will break down. A society where red is white sometimes and black other times and blue again later and so on will be chaotic. This shows that truth telling is a moral requirement for a society to function well. This is the reason why you do anything you want or you speak anything you want, and truth telling is never ever a moral requirement is never ever going to work. Thus, 'thou shalt not tell lies' is a moral requirement for a society to function.
Now this does not mean that there is no qualification to the statement. Sometimes in certain situation telling a lie may be a requirement. For example, when a Nazi's Gestapo comes home and asks if there is any Jew hiding inside my cupboard, instead of telling them that there are ten Jews hiding inside, I may tell a lie. In such situation telling a lie will be the lesser evil. But just because there is a condition that opens up the door where lying is justifiable, that does not mean that the principle 'thou shalt not tell lies' vanishes. The principle just gets modified little bit: thou shalt not tell lies under normal circumstances but for situation where lying will prevent unjustified killing or something of that sort.
But there are other moral principles that stand firm irrespective of cultures. For example, something like 'You cannot cut off your children's head just for fun'. Now one may say that no one does that sort of things. True. But no one does that sort of thing because it is considered to be wrong. Moral inquiry is not only about human action; it is about human inaction too. And human species perform action A or B or C, and not K or L or M or N or O or... because only A or B or C are justifiable. The rest are all unjustifiable. There are many features of human action whose acceptability changes over time; but there are many features of human inaction whose unacceptability remains unchanged over time.
Given this nature of morality one can meaningfully contend that the moral worth of certain human actions/inactions remains unchanged or ought to remain unchanged though the moral worth of certain actions change over time.
PS: The question whether lying is inherently wrong or whether it is wrong because indiscriminate lying effects breakdown of society is an interesting point. I am not getting into that point here because my concern here is just to show that moral relativism does not work.
PS: The question whether lying is inherently wrong or whether it is wrong because indiscriminate lying effects breakdown of society is an interesting point. I am not getting into that point here because my concern here is just to show that moral relativism does not work.