I have noticed a lot more status/hierarchy jostling from immigrants who come from certain cultures. But I don't see that in their children who tend to have a much more western view of status/hierarchy.
The second generation Asian Americans I know aren’t quite as hierarchy-focused as say my parents. But they’re also nothing like my wife’s Oregonian family that’s been in the US for hundreds of years. (Among whom having status is almost something to be embarrassed about.)