According to A People's History of the United States, why was it feared that the whites would join slave revolts?
To understand why this would be so, think about an analogy in our modern world. Let us imagine that a union was going to go on strike. Would we think that it was strange if its black members and white members both went on strike? We would not think this is strange because we would think that the black and white workers had the same interests and shared a similar experience that made them want to go on strike. The same was, at least potentially, true in colonial America.
In colonial times, many white people were treated in ways that were not all that much different than how slaves were treated. Among these were indentured servants who were unfree just as the slaves were, although the indentured servants would become free after a given term where the slaves would not. Plantation owners treated both groups badly. Even poor free whites could have felt more in common with exploited black slaves than with the rich plantation owners.
Thus, it is not too surprising that whites would have feared that lower class whites (and especially indentured servants would join slave rebellions. As Zinn says in Chapter 2,
In the early years of slavery, especially, before racism as a way of thinking was firmly ingrained, while white indentured servants were often treated as badly as black slaves, there was a possibility of cooperation.