We can explain what Dalton Conley means when he says that "race and class are nothing more than a set of stories we tell ourselves to get through the world" in the following manner:
Conley means that race and class do not really exist in the natural world. They are social constructs created by society with the purpose of categorizing and classifying people.
By doing so, we can distinguish people depending on the amount of money they have or the color of their skin. The purpose is to create a sense of us vs. them, of difference, of some being better while some are worse.
Race and class should not - and do not - define a person's worth. We are all humans and should be seen and treated equally. Race and class prevent true equality from taking place.
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