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I can see the rationale behind Haidt's argument and now that I think of it, yes, people do undertake ex-post-facto explanations of moral intuitions. Yet, there can be ways to overcome the "futility of moral arguments"

In his article he mentions the reasoned persuasion link that 'works not by providing logically compelling arguments, but by triggering new affectively valenced intuitions in the listener'. This would work as a way to get your side of the argument into the other side. Since people only listen to what validates or proves something they already believe in, we can tailor our argument such that it can convince people in a subtle but effective manner, by appealing to their judgement, yet sticking really to your own.

Haidt also mentions that to be one has to reason like a lawyer, not present the truth, but defend your argument. If people are presented with other sides or 'roles' in the argument they change their mind. If one is meant to empathize with a certain person in a situation they were morally against they can turn their favor towards it by putting themselves in their shoes.

I believe that these and other techniques make moral arguments interesting and challenging, and far from futile.