I don't care whose position it is and I apreciate your effort to explain it, no need to apologise.

Regarding the point itself, rich people or higher classes people as a group also have "institutional power", much more than white people as a group. It is pretty easy to differentiate people background after some sentences as the research shows. So the only difference between those two disadvantages is exchanging some words. Even if it is a significant difference, it still doesn't change or cancel other circumstances in a person life and doesn't make this difference overruling any other difference.