Kind of depends how you define moral skepticism. Seems to be some debate on the precise meaning. Seems to me if youre coming at morality with the presumption that moral knowledge cannot be known with any certainty then youre putting the cart before the horse and are asking a loaded question. If youre coming at it from the perspective that morality doesnt exist innately or that it is just a human construct then you also presuppose the answer to your own question. Or by moral skepticism do you simply mean any moral claim can be questioned or may be contingent on having a greater understanding of circumstance?
Do you want me to regurgitate other peoples philosophy, that could easily be read in a book?
Personally Im of the opinion only one of two things can be true about morality. Either one, it doesnt exist whatsoever and there is no point discussing it. Or two, it exists absolutely/objectively, and is not open to relativism.
I say that because I make a simple observation. Nothing in this universe that exists and that matters outside of the individuals own experience (i.e. has a bearing on others or on nature, i.e. is impactful in any meaningful way) is relative. Everything in this universe that exists is absolute.
Trees, clouds, if you want to be specific. Logic, physics, if you want to be more abstract. Even mathematics and logic themselves. These are arguably man made constructs, if you prefer to think of them as such. But even they are absolutes. The laws of physics. The laws of nature. I challenge you to point out just one thing in this universe that we can all agree exists (even as an abstraction) AND has a meaningful and real impact on the world outside, but is relative/subjective rather than absolute/objective. I challenge you to find me at least one example.
If morality is the sole example to the rule that you can find then one must question why it ought to be so, and whether or not it is so. I see no good reason morality ought to be the only exception to the existence of abstract notions impacting real events and social interactions that just happens to be subjective.
Sure, your tastes in clothing style or flavored ice cream may be considered "subjective". But is it relevant in any way? Does that impact my life? Does it have repercussions to physics, or to human social interaction? Subjectivity of this nature may exist, but it exists strictly confined to the individuals own unique experience, and has no impact on the objective world. One cannot say the same of mathematics or of morality.
Im trying to define a sort of "realness" here. Morality is real because it governs peoples actions and reactions and social structure. It impacts human nature and human interaction. Its fair to say that as an abstraction it is real in some way. Do real things exist subjectively? I dont think so, I have never seen such a thing, except maybe only morality.
If morality is subjective/relative then it cannot exist, because any abstraction that doesnt hold a consistent set of universal rules is completely arbitrary and meaningless. Imagine if logical truth were a cultural or individual phenomenon and conclusions didnt transcend cultures or borders. It would be an absurdity, wouldnt it?
I recognize that different cultures and religions DO have different moral values. But there is a difference between having the rules right, and only believing that you do. Morality is perhaps one of the greatest human intellectual endeavors. Its a work in progress. We are uncovering truths all the time, and we learn and grow and change. Id like to think that we are uncovering moral truths and refining our values and will eventually "get it right", in the idealized distant future. Thats not to say anyone has it right now... perhaps different groups have caught a glimpse of different true parts of the whole.
Point being, being ignorant of the whole truth doesnt make the truth relative. It makes knowledge relative, but that could only result in false conclusions. Saying that the truth is relative because knowledge cant be certain is an appeal to ignorance, and its usually done in order to rationalize the individuals version of morality, rather than to give cause to question it. You see it with the abortion advocates: "we cant know with certainty whether its right or wrong so lets default to the most liberal position with the most dire of moral consequences." Ignorance used as a tool in its own right is, in my opinion, an act of immorality in itself.
The observed existence of relative morality doesnt validate relative morality. It could very well be the case that all cultures are slowly evolving their sense of morality, even independently of one another, gradually converging onto a single moral truth. It could also be the case, if youre of a Biblical persuasion, that all of humanity started with a single morality and our corruption has created the divergence in the first place. The point is, the existence of the various moral norms in no way legitimizes moral relativism as the true way morality should be viewed.
I would argue that moral relativism is rooted in the biases of the individual, and a need they have to feel justified and vindicated in their self-serving interests. The notion of "tolerance" was advocated not by good moral people but by those operating outside the moral norms and demanding their lifestyles be accepted by society.