You said
> I have trouble understanding why a dead person would care about anything after their death
Examining the unstated implications of your argument, taken on its face, is not the same as moving the goalposts. Saying "I don't care what happens after I die, so no need to even ask if you can take my organs... except hang on, no, don't abuse my body in weird ways, I'm not okay with that"–THAT'S moving the goalposts.
> it's hard to see it as a bad thing to help the living
except to the extent that 1) harvesting organs from political prisoners is just about as close to a bad thing as you can imagine, and 2) even if we're not talking about China in particular, involuntary organ extraction harms the dignity of living kin.
> Imagine if the relatives have racist objections to donating an organ, and let someone die because their own feelings would be hurt if they saw a person of the "wrong" race being helped. How do you weigh their racist feelings, versus the life being saved?
The right to bodily integrity, to the choice about how your body is used, is unaffected by your motives. A right does not cease to become a right once you disagree with how someone wishes to exercise it.
You don't want your organs to go to a black man? Exercise your right to bodily integrity by not agreeing to be an organ donor.