I don't believe in the concept of "natural law", at least not the way you are using the term. I don't think that there is anything inherently evil about murdering or raping another person, in fact I think you could probably make a case that murder and rape are "natural". Of course I would never murder or rape another person myself, but that is more of a moral choice on my part. Although I do hold this as a "personal natural law" ie a moral, I do not assume that this personal law needs to be applied to the public.
In any given context you are either a moral relativist or a moral absolutist, right? There is no middle ground, it's a dichotomy? In this day and age, especially outside the context of your own culture/society, I think that it is extremely important to be a moral relativist.
In the context of society, I am a moral relativist. In the context of my society I don't even think in these terms. I do what I feel is right/good. I guess this is the empathy you speak of. I just limit these value based decisions to places/people that I know will appreciate them.
I think we can both agree that both absolute moral relativism and absolute moral absolutism is inherently dangerous. As with most things, it comes down to a balancing act.
Do societal moral relativists hold an obligation to cure social malaise even if they themselves don't perceive it?
Do you think that if moral relativism goes unchecked it would lead to mass murder/rape?