“Religion yes, clergy no…. As we did without clergy, let us do without soldiers.” What impact did that have on society?
I'm not entirely sure what this question is asking, so I'm going to treat it as though it's asking about the significance of this quote in the overall story.
In this very strange short story, Ursula K. Le Guin describes what a utopian society would be like. In this quote, Le Guin tells us that this society wouldn't have either clergy or soldiers. Since both religious people and the practice of war can be large sources of conflicts in a society, Le Guin presumably provides this detail to further support the idea that Omelas is perfect and peaceful.
The distinction between clergy and religion is an interesting one. Le Guin hints here that religious beliefs themselves aren't what typically cause conflict in today's world and that the people who practice and enforce religion are instead most often the sources of conflict. Thus, in Omelas, while people are free to believe in religion, there are no religious authorities to monitor the people. Le Guin leaves a lot unsaid here, leaving it up to her readers to further examine this idea on their own.
Whether Omelas is peaceful because it doesn't have clergy or soldiers, or whether it is already so peaceful that it simply has never needed clergy or soldiers, is unclear. Again, Le Guin leaves this question for her readers to decide for themselves.
At the end of the story, Le Guin reveals to us that there is one terribly ugly and evil thing in this society (I won't spoil it for you! You should read it!). Thus, the quote about clergy and soldiers is significant in the overall story, because it presumably tells us that in order for a society to be "perfect" and do without authorities such as soldiers or clergy, there still needs to be one ugly, terrible truth beneath everything else. Is Le Guin saying, then, that societies need to have authority figures in order to succeed? Is she saying that there can never be any perfect society after all? It's unclear. The real beauty of this story is the plethora of questions it leaves behind.