After reflecting a little, I came to the realization that inclusion of these two characteristics conflicted with the curators' efforts to make the case for human evolution. That is because careful thought about these unique qualities of human beings would tend to undermine belief in a neo-Darwinian explanation of human origins. Let me explain why.
Consider the first characteristic--that humans believe that there is such a thing as right and wrong. It is difficult to dispute that the vast majority of people over the long course of human history have believed that some things are good and some things are evil. Even those (mainly, in the last few centuries) who have denied the objective existence of right and wrong have generally acted as if there are such things as moral facts. The question is: where did this idea of right and wrong come from? The idea of morality cannot have come from nature as nature is essentially amoral (animal behavior is not generally motivated by moral principles). The standard evolutionary answer is that morality developed as a means of ensuring the survival of the human species. However, there are arguably some acts that could be viewed as helpful to the survival of the species that we would view as immoral. For example, in some instances rape could be one way to ensure the reproduction of more humans (and thus perpetuate the species), but I am fairly certain that we would agree that this would not make it right. But why would we feel that way? I think the answer is that at some fundamental level we believe that it is wrong to hurt others, whether physically or emotionally. In another way, we could say that it is wrong to violate the inherent dignity of other human beings. But why? I would contend that this notion of the inherent dignity or worth of human beings is rooted in the belief that humans were created in "the image of God"--an idea that is in direct contradiction with neo-Darwinian evolution.
What about the second characteristic--that humans can write equations and poetry? That human beings are able to grasp highly abstract ideas like those contained in mathematics and are able to manipulate language in the highly sophisticated way demanded in poetry is a reflection of the great powers of the human intellect. No other species is able to do such things. And yet, according to standard evolutionary theory, we share our ancestry with other organisms which are incapable of such feats. How can this gap in intellectual abilities between us and them be explained? Is it really likely that the passage of even millions of years and the workings of random genetic mutations could produce such a remarkable difference? Or is it more likely the case that our differences with other living things is due to our fundamentally different status as those created to reflect the nature of our Maker?
In short, the Smithsonian's explanation of what makes us human is at odds with the narrative it promotes about human origins. However, I suspect this never occurred to the museum staff who created the exhibit. I have noticed that those convinced of the truth of neo-Darwinian evolution tend to be blind to anything that challenges that orthodoxy.
John Gurche's reconstruction of australopithecus afarensis, a supposed ancestor of humans, on display at the Smithsonian. Image from Wikipedia.org.