The riots in "Once Upon a Time" represent the outside world that threatens the fairy tale life the family lives.
In telling her "bedtime story," Gordimer constructs a tale of a family living the perfect life. Their world is the fairy tale world: "In a house, in a suburb, in a city, there were a man and his wife who loved each other very much and were living happily ever after." The family keeps the outside world at a distance to protect this flawless existence. Through examples such as the purchase of different types of insurance policies and the gate with the sign reading "YOU HAVE BEEN WARNED," the family does their best to keep the threats of the outside world away from their lives.
The riots represent a part of this outside world that the family does not want to acknowledge. The riots are a reality that the family wishes to avoid. By insulating themselves from worldly elements such as riots, the family does not want to acknowledge "the other" that lives alongside their idyllic world. The riots scare them because they embody the uncertainty, discomfort, and danger that the world can pose. They symbolize a part of existence that the family cannot control and from which they wish to retreat.