Earlier quoted context omitted.
There once was a study where they eloquently demonstrated this by putting the same white actor into two situations: one had him lay down acting like he was dying from a hear attack in front of Wall Street wearing a suit. The other had him doing the same thing but wearing worn out sports clothing. They found that people responded more favorably to the actor when he appeared to be of the same social class.
We can thank the wars against poverty, drugs, homelessness, and crime for this. These all serve as foils against considering ones own class and how easy it is to move downwards in America without any support for those not in abject poverty nor consideration for the disappearance of community building locations, events, and organizations, in large part due to union busting.
I say this because the kind of prejudice you point out is rampant across all societies, not just America and if anything, America handles it a lot better than any other society.