Elites don't promote racism because they're racists, they promote racism because it's a mechanism of control.
Racism as a theory is pseudoscience bullshit. There is no scientific basis for race even existing. We're all humans. The only people who believe otherwise are the victims of propaganda.
See also: https://slatestarcodex.com/2017/06/21/against-murderism/
> I fail to see how the citizenship test would lead to the rich getting richer.
It could benefit them if the subset of people it prevents from voting would vote for things they wouldn't like.
Also, some policies are nothing but collateral damage. Elites get the proles fighting each other and each coalition starts demanding aversarial policies that harm the outgroup and neither hurt nor help the elites, but keep everyone distracted and fighting each other. The elites don't care which policy like that is implemented as long as it keeps people too busy fighting each other over it to pay attention to certain other things.
It benefits the rich because the proponent-victims spend their political capital to implement the policy and then the opponent-victims spend their political capital to repeal it instead of either of them spending that political capital to do anything that benefits the poor at the expense of the rich.