The core symbols are the central elements to the story: the blindness and the cathedral itself.
The blindness is literal for the blind man, but the narrator is emotionally blind and alienated; it seems like he's more cut off from the world than the blind man.
The cathedral is an extended symbol for the difficulties of communication in an alienated world. The sighted man wants them to share the same reality, but religion (which was traditionally a unified factor, and one that transcended differences) means nothing to him. So he has to fumble his way along by touch, essentially the blind leading the blind, in an attempt to communicate.