Which principles of utilitarianism would you connect to the theme of the short story?
Utilitarianism's "core idea is that whether actions are morally right or wrong depends on their effects," and specifically, among types of utilitarians, "rule utilitarians focus on the effects of types of actions" that result from the adherence to a rule.
What is at work in LeGuin's story seems to be rule utilitarianism. Rule utilitarians believe that if an action is correct, its outcome is the greatest good for the greatest number. Since imprisoning the child in a windowless cellar, feeding it only enough to stay alive, and denying its humanity facilitates the well-being of Omelas's citizens, they are at peace with their rule, as incomprehensible as it might seem to those with a different guiding philosophy.
The narrator explains that "they all know it is there, all the people of Omelas. Some of them have come to see it, others are content merely to know it is there. They all know that it has to be there." The people of Omelas understand that all that is good in their society can only be maintained through the barbarism of the neglect of the child; this action leads to the greatest good, the best result. The society has come to accept the cruelty as necessary, and those who agree are the people that stay in Omelas and accept the paradox of their comfortable existence.
Those that cannot accept what they know about the necessary evil or rationalize that the rule offers the greatest benefit to the greatest number of people are the ones who walk away from Omelas.
I think that one can see a pretty strict form of utilitarianism represented by those who live in Omelas. The reality is that all of the citizens fully understand that their happiness and state of being is contingent on this child being miserable. They grasp that the child's suffering is key to their own happiness. The entire social order of Omelas is one where individuals must live with the suffering of a minority of one in order to gain the greatest sense of happiness. In this setting, the rights of the majority has subsumed the rights of the minority. At the same time, it is asserted that helping the child out of such a predicament is both futile because the child would lack the understanding as to what to do and also endangers the Omelan society, in general. This would mean that attempting to help the child would actually do damage to the greatest good for the greatest number. A fairly strict reading of the philosophy might render this view.