Ultimately, I don’t think objectivity has anything really to do with morality. Our moral code rests upon how particular actions make us feel — the emotional and physical impact our own behavior and the actions of others have upon us both individually and collectively. While it is possible to “objectively” confirm many if not all of these impacts through various means, the fact remains that the impacts being confirmed feel like something to each of us as individuals. This is as true for those on the receiving end of the injustice as it is of those facilitating it and those merely witnessing it.
Taking slavery as an example, I would argue it isn’t wrong because we can objectively verify the immorality of it. It’s the subjective experiences of the slave(s) that make it wrong. These experiences can be documented quantitatively as well as qualitatively, of course, and this documentation is critical to formulating strong arguments against slavery. But ultimately the sense of repulsion most of us feel when we witness extreme acts of cruelty/oppression is grounded in our own subjective experience of the injustices being witnessed. Even when not directly on the receiving end of cruelty ourselves, as social creatures we are biologically programmed with an ability to place ourselves in the other person’s shoes and imagine how we would feel if being subjected to the same treatment. To suppress this instinctual repulsion we must engage in the dehumanization of the other person through various means. We must convince ourselves that we are “morally justified” because the cruelty is for the “greater good” or because the other person “deserves” the treatment they are receiving, etc. However, as our concepts of humanity have grown beyond our own local tribe, religion, ethnic group, and nation this kind of dehumanizing has become increasingly difficult for us to collectively maintain.