In Leslie Marmon Silko’s Ceremony, the hazel eye color is actually pretty significant. One of the major themes in the story is the Native American struggle to maintain their culture from the colonialist invaders' oppression. This is where the hazel eyes are significant.
The presence of hazel eyes in a Native American in Ceremony means that the character is of mixed ancestry. This made the characters with hazel eyes stand out from the rest of the tribe, thereby othering them. A character with hazel eyes was also more likely to have progressive views. Night Swan and Betonie both spoke of change approaching, and they both had hazel eyes. Being of mixed heritage, they would be frowned upon by the more traditionalist members of the tribe, but they knew it was only a matter of time until new ways crept onto the reservation.
At a time when their culture was being destroyed, those with hazel eyes could have been viewed as a symbol of the white invaders and the oppression of Native American heritage. The meaning behind the hazel eyes becomes much clearer the more one analyzes the work.
eNotes has some great information on Ceremony which can help you further your understanding!