A school that explicitly stated they only want the kids of the upper classes could just say they want rich white kids, but they'd be savaged in the media for admitting the truth.

So instead there's tons of handwaving about how the most important predictor of success in life and in education is experience in the sailing club and the polo club and the chess club. Not because its true, but because mostly rich white kids are in those clubs so if you select those groups you'll get the "right" people wrt race and income.

The problem is someone fakes their social life and interests to get into school, if they make it they're going to be surrounded by a weird mix of genuine upper class kids who really did grow up enjoying sailing and playing polo, and a subgroup (perhaps too small to be self sustaining and supportive) of poseurs who don't care about that stuff other than a means to an end.

There is an analogy in software hiring practices. Obviously everyone knows from studies that higher IQ people are more successful. But implementing IQ tests is a legal minefield. Smart people can learn algos. So google does or used to torture applicants with algo questions. They're not looking for people who know all about red black trees or implying that all jobs there use algos, but are selecting people who passed the "IQ test that isn't an illegal IQ test" filter. "cargo cult" copycat companies who do almost the same but miss the intelligence test part, perhaps by asking brainteasers or similar tasks that don't require intelligence, are comical.

The moral of the story, is if you want to do something wrong or immoral or highly politically incorrect, you can get about the same outcome by playing games with overlapping venn diagrams and pretend that a right, moral, popular activity with a large overlap is what you "really" want. A large part of adult/older human cultural interaction is understanding when someone's talking exoterically or esoterically in order to respond correctly.