III. The argument from reformers:
1. If moral values are subjective, then moral codes cannot improve, since there is no objective standard by which to judge one code better than another.
2. But the work of people like Martin Luther King and Rosa Parks shows that moral codes can be made more just.
3. Therefore, moral values are objective rather than subjective.
The weak point here is in premise 2: how are we to decide if a moral code has become "more just"? There were many who opposed the civil rights reforms, who thought it was a move away from true morality rather than towards it. Likewise, there were many Germans who applauded the moral "reforms" of Naziism. The fact that it is possible for moral codes to change does not imply that they are improving. I think it would only be possible to claim that a particular reform has made things objectively more just if everyone agreed that that reform was an improvement - and this just returns us to the considerations of argument two.
The fascinating question of how moral codes change and why seems to get neglected by moral philosophers. There is a great discussion of the issue in Alasdair MacIntyre's After Virtue. MacIntyre says moral codes change when they encounter challenges (from encounters with other societies, or from considerations that arise internally) that reveal the existing code to be inadequate according to its own standards. (His view is reminiscent of Kuhn's view of scientific revolutions.)
Such a view of moral codes as constantly evolving and interacting doesn't rule out objectivism or absolutism, but neither does it require it.