The main thrust of your objection is to insist that my argument, if successful, would prove too much. It would prove that questions of beauty, fashion, and flavor are objective. And of course those questions are not objective, so clearly my argument must have gone wrong somewhere.

Yes. Correct.

What do disagreements about morality look like? They usually look something like this: ...A: No, you're wrong, because to lie to someone is to treat them as a mere means, which is never acceptable. B: No, that is sometimes acceptable, because the only real good is happiness, so we can treat someone as a mere means as long as it's for the good of happiness. [And the argument continues this way.]

First, the individuals disagree about whether lying is wrong. That disagreement is rooted in different assumptions about whether it is right to maximize happiness or to respect beings as ends-in-themselves. That disagreement cannot be resolved without referring to some justifying assumptions for which one moral assumption is to be preferred over another. Why follow utilitarianism v. kantian ethics? You don't have to follow either of them. You can choose to, based on your preferences. That's what the argument would come down to. An individual thinks the world created by one or the other model would be more preferable. This argument necessarily ends the same way you ended the flavor argument: a difference in subjective opinions about what is desireable as acceptable and unacceptable social behavior.

What do disagreements about flavor look like? They usually look more like this: C: Well, not to me. D: Oh, okay. [And there is nothing left to disagree about.]

You've framed these arguments totally differently. Try this:

C: This cake tastes good.

D: No it doesn't. It's dry.

C: Dry cakes are better tasting than moist cakes.

D: No, moist cakes are better tasting than dry cakes. [And the argument continues in this way]

There might be cases where C bullheadedly stands his ground and says that D is mistaken (or vice versa). But in this case C would plainly be behaving irrationally: he wouldn't be disagreeing with D's claim ("It tastes like soap [to me]"), he'd just be refusing to believe D's report of her own gustatory experiences. And of course D is the expert about her own gustatory experiences.

This is correct, and equally applicable to morality. I believe X is right, and you believe X is wrong. We are only justified by the moral framework we assume. But which moral framework should you assume? There are infinite possible standards to use to make that decision. Which standard you use must itself be decided by a moral standard, ad infinitum. At some level your decision to adhere to a given moral standard is rooted in a free decision based on personal preference.

In the case of moral disagreement, however, there's no obvious irrationality in continuing to argue.

Not where you left the argument off. But if you keep going there is. Why choose utilitarianism or kantian ethics or virtue ethics etc.? At some point, it becomes a matter of what sort of world you want to create.

“Okay, you might get that soapy taste, but we're not talking about soapy tastes. We're talking about what tastes good." Does that even begin to make sense?

This whole cilantro example is a bad example. That's a biological difference between people. They're fundamentally not making judgments about the same experiences – which is vital. Try my cake example. They both have the experience of a dry cake, but they perceive it differently as tasty or non-tasty. Similarly, two individuals can have the experience of money-lending and usury, but they perceive it differently as moral or non-moral. Which perception is right? Is the cake actually tasty or non-tasty? Is usury actually moral or non-moral?

So the relevant difference between arguments about morality and arguments about flavor is that we are obviously and undeniably behaving irrationally when we argue about flavor

I don't agree with this. If we both carry similar assumptions about what is tasty (i.e. we both like spicy, indian food, with a bit of sweetness), we can use those standards to argue about what is or isn't tasty. Similarly, if we both carry similar assumptions about what is right (I.e we both believe utilitarianism is right), we can use those standards to argue about what is or isn't right. But in both cases what assumptions/standards we use are rooted in a personal choice and preference.

but we are not obviously and undeniably behaving irrationally when we argue about morality.

Morality works exactly the same way as taste, as I stated above.

First, you could produce an example of an argument about flavor (or about fashion) that resembles the argument between A and B much more than the argument between C and D--that is, an argument about flavor (or fashion) that seems to proceed without reference to the subjective experiences of pleasure and displeasure.

I think I've done this successfully.

Or second, you could argue that I've misrepresented what moral disagreements really look like, and that a good analysis of moral disagreements will reveal them to look just like the argument between C and D, so that we are obviously and undeniably behaving irrationally when we argue about morality.

I've also done this successfully. I also outlined in abstract why the structure of the nature of disagreement in morality and flavor and fashion is necessarily rooted in subjectivity.