How does symbolism establish the theme or conflict in "By the Waters of Babylon?"
I am not actually sure that symbolism has much to do with establishing the theme of this short story - far more valid and important to working out the theme is the setting, so in my response I will focus on this.
This masterful dystopian short story is used a lot in English teaching to give an excellent example of 1st person narration, where a character is telling you the story directly, and you can only see the action through their eyes, contrasted with an omniscient narrator who is god-like and all-seeing and can tell the reader what every character is thinking and feeling. This form of limited narration is used to great effect by the author as we literally go on the journey with John, seeing and feeling what he sees and feels, and we gradually piece together like a jigsaw puzzle what is going on, where we are and what has happened.
This narrative technique greatly serves to emphasise the message or theme of this story. We slowly begin to work out the many clues that there are (such as the names John gives things like "god roads" and what the sign "ASHING" rally said) and realise that this story is set in a post-nuclear war world which has been decimated, and the inhabitants have sunk back into the dark ages. John and his tribe describe a primitive world with many threats and mysteries that they do not fully understand. However, during the course of his journey and the vision that he has in "the high towers of the gods" John reflects the moral of the story: "Perhaps, in the old days, they ate knowledge too fast."
This then is the brutal warning that the story gives: we live in an era of unprecedented scientific discovery, yet we risk discovering too much truth too quickly, and opening some terrible Pandora's Box or using scientific advances before we fully understand their consequences. One only has to look at the press today and issues such as stem cell research, the human genome research project and cloning to see that the danger is still here and Benet's short story is still just as applicable in today's society. Whether we take heed or not is another matter...
Thus it is the setting far more than the symbolism that to my mind plays a vital part in establishing the disturbing theme of this story. Whilst of course there are examples of symbolism, these are secondary when it comes to the theme.