To me, there are two major conflicts within John during this story.
First, there is conflict in his heart or his soul about going across the river to the forbidden Dead Place. He solves this conflict simply by mastering his fear. He just decides that he will not let the fear stop him.
Second, there is a conflict within him as to what lesson he is going to take from what he sees in the Dead Place. Will it make him lose faith when he learns that the gods were really just people? He resolves this, instead, by having faith in people and saying that they will learn to build again.
To me, this story is about the conflict between truth, as it is found in the stories and legends that shape a culture, and the desire to learn new things, even at the risk of undermining "truth" as one knows it. On the surface, the conflict John must overcome is his own fear of crossing the river, but the source of that fear isn't just the fear of the "gods" he has learned from his father but, more importantly, his fear of his own thirst for knowledge. His dream of the dead places is "strong," his father says; it may "eat you up," and in fact John's curiosity about the ruined city is too great to overcome. When he goes to the city and learns that the gods really were simply men like himself, he has to rethink everything he has learned from his father. He realizes that, rather than fear the knowledge of the gods, his people must work to reclaim it and rebuild their cilivilization.
The conflict of the story is that John must over come his fears and go to the city. This is needed for him to become a priest. He must go explore the city.