Well you would have to demonstrate that last statement at least to dispel what looks like you a)not being really interested about how you arrive at a decision that is, as you put it morally correct b) show that somebody who holds a separate point of view is invalid morally in that view.
For myself, ideally, when I say something is wrong, my first reaction is of something which offends my nature. The wrongness I feel might take the form of disapproval, disgust, abhorrence, even fear, depending upon the situation. I then try to assess the wrongness of the situation according to my values,( which may well have their origin in my culture and my upbringing). in as rational a way as possible(e.g. by trying to ascertain as many facts regarding the situation as possible or by trying to consider in as level headed a way as possible the points of view of others.) The result of all this is something which I would call my moral opinion which I see as correct for me. Because I don't see morality as something written in stone, I see it as quite possible for a person to hold an alternative moral opinion which they regard as the correct one for them. If you take that as not being interested so be it, but I certainly don't see it that way.
No source of mathematical realism has been found. It just operates Moral irrealism doesn't work because there is no arbitration within it to say what is right and what isn't and with such a basic and obvious flaw surely one has to start looking elsewhere. Beyond that, if morality is just a question of opposing but equal values the value difference is zero and the value of morality is zero and when one criticises other's moral decisions one is play acting. That you're not playacting points, IMV, to a subconscious assent of moral realism.
I really don't see any pertinent linkage between morality and mathematics. One is very much dependent on and associated with feelings and opinions, the other on logic. One is ephemeral in that moral attitudes can change and disappear as people die, the other is based upon such things as equations and formulae which remain as intrinsic in their own right after people die.
The arbitration, as you call it, comes from the collective agreement of a society, which changes and shifts as that society changes, often as a result of one group trying to influence another group in order to change their moral stance. If this were not so then we would expect morality to remain the same thoughout history. This is not so.
I have an opinion that same sex marriage is as acceptable as heterosexual marriage. I would hope that this is a universal opinion.
I have an opinion that assisted suicide should be enshrined in law. I would hope that this is a universal opinion.
I have an opinion that stem cells from human embryos should be used in medical research. I would hope that this is a universal opinion.
The fact that I would wish my opinions to be universal is not some sort of evidence for saying either that they are universal or that they are objective. It is only evidence that they are my opinions.