With respect, I think you are slightly mistaken in your conclusions about this story. You are right in thinking that there are two groups of characters that are presented: those who stay, and those who decide to walk away from Omelas, the obvious subject of the story as indicated by the title. Yet, it is clear that they do not choose to leave because of any problem with class. It is made clear that those who choose to leave are not from any specific social grouping. Rather, those who leave appear to be reacting to a gut response that protests against the treatment of the child who is the source of the happiness of Omelas. This story is therefore not much about class. Rather, in this story the author is presenting us with an extreme moral dilemma. Is happiness for the many justified by extreme suffering and punishment for one individual? Note how the text posits this conundrum:
If the child were brought up into the sunlight out of the vile place, if it were cleaned and fed and comforted, that would be a good thing, indeed; but if it were done, in that day and hour all the propserity and beauty and delight of Omelas would wither and be destroyed.
Thus the two groups of characters who are referred to are those who hide and ignore there feelings of injustice and focus on "the greater good," and those who just are unable to accept such a Faustian pact, and are compelled, by moral forces beyond their control, to leave the city as an act of protest, in search of a better world which tries to attain happiness for all, rather than happiness for most at the expense of the one.