At risk of triggering the political mind-killer, I think there are some potentially problematic consequences of this view.

Once a disagreement is known to result from a pure difference in values, there isn't a rational way to resolve it...the best we can do is make people aware of the difference in their claims.

Suppose we don't have good grounds for keeping one set of moral beliefs over another. Now suppose somebody offers to reward us for changing our views, or punish us for not changing. Should we change our views?

To go from the philosophical to the concrete: There are people in the world who are fanatics who are largely committed to some reading of the Bible/Koran/Little Green Book of Colonel Gaddafi/juche ideology of the Great Leader/whatever. Some of those people have armies and nuclear weapons. They can bring quite a lot of pressure to bear on other individuals to change their views to resemble those of the fanatic.

If rationalism can't supply powerful reasons to maintain a non-fanatical worldview in the face of pressure to self-modify, that's an objection to rationalism. Conversely, altering the moral beliefs of fanatics with access to nuclear weapons strikes me as an extremely important practical project. I suspect similar considerations will apply if you consider powerful unfriendly powerful AIs.

This reminds me of that line of Yeats, that "the best lack all conviction, while the worst are full of passionate intensity." Ideological differences sometimes culminate in wars, and if you want to win those wars, you may need something better than "we have our morals and they have theirs."

To sharpen the point slightly: There's an asymmetry between the rationalists and the fanatics, which is that the rationalists are aware that they don't have a rational justification for their terminal values, but the fanatic does have a [fanatical] justification. Worse, the fanatic has a justification to taboo thinking about the problem, and the rationalist doesn't.