Does objectivity matter?

In a fit of procrastination, I read this paper, and found myself entirely unconvinced, for reasons (oddly enough) related to my increasing sympathy for some elements of the Kantian view of ethics.  Enoch's central argument is that disagreements in mere preferences should be handled impartially, but there are moral disputes that should not be handled impartially, so moral disputes can't be disagreements in mere preferences.  I can see a major wrinkle he doesn't appear to consider, though.  It makes little sense to deal impartially with others who are unwilling to cooperate; everybody needs to be impartial, or it doesn't work.  But the very example Enoch gives where someone is morally required to stand their ground and not be impartial is one involving the status of women; presumably he's imagining that an enlightened individual is confronting one who thinks women should be regarded as inferior, and saying (rightly) that the enlightened individual should stand their ground, but obviously the unenlightened individual is precisely guilty of not being impartial.  So there is a reason for the enlightened individual not to regard the matter impartially (he can't; trying to treat the other's view as having the same weight as his own involves giving weight to the other's partiality, and so if he tries to be impartial he'll automatically fail), and it doesn't require regarding the disagreement as more than one of mere preferences.  I do not think that this is merely an accidental feature of the example Enoch chooses, either, though I'd have to do more procrastinating than I really should to go into that in detail.