Harrison's parents are not emotionally affected much at all by the death of their son because they cannot be.
For Harrison's mother, Hazel, her "perfectly average" intelligence does not allow her to become emotionally invested in much of anything. Even when she speaks to her husband in a caring manner about his health, it is quite shallow. She calls George "honeybunch," but the word feels void of emotion. Hazel's intelligence only allows the most basic of human responses. Even when the story reveals that Hazel has cried after viewing the death of her son, Vonnegut makes it clear that she cannot sustain thought or emotion by including this exchange between George and Hazel:
"You been crying?" he said to Hazel.
"Yup," she said.
"What about?" he said.
"I forget," she said. "Something real sad on television."
Harrison's father, George, could be emotionally affected by the death of his son if he did not have to wear the government-issued handicaps that keep him from feeling deeper emotions and thinking deeper thoughts. Because he has been handicapped due to the government's desire to make society completely equal, he cannot muster up any thoughts or emotional reactions that would be better than the lowest common denominator's thoughts and emotions. When George starts to think and feel, incredibly distracting sounds stop his flow of thoughts. It's not that he does not want to feel emotional about his son's death, he just can't.