Nope, it doesn't go both way. Racism and classism only go one way, which is towards the poorer or more vulnerable part. Pick on the weaker is a sign of cowardice. Do the same on the stronger is well-accepted, and rightfully so. Always punch upwards.
Not all whites or blacks are the same. Hating someone you know nothing about due to race is racist, full stop.
The rule of averages don't apply to individuals. You can't beat a poor X child and call it punching up, because they are part of Y race.
But I'm pretty sure the Afro-American population would gladly swap 50% of black NBA players to have 50% of them in the middle-class.
P.S. I disagree with you
A couple famous chilled dudes prescribed to not punch at all. The ones I'm thinking of were referring to Romans and British colonisers, but I suspect they'd have applied it to white rich buddies as well.
(Please note that I didn't write what I think of it, I'm only fuelling the debate)
Even though I mostly take a "white X" as a metaphor for a lack of diversity (of opinions and mindsets), I don't think most people do. These people aren't assholes because they are "white X", they are assholes because they are bourgeois stuck in their echo chamber.
Class seems to be the determining factor, really. Europeans had a couple environmental advantages early on [0] that allowed them to monopolise the world's resources, which were never fairly redistributed.
The current bourgeois are bourgeois mostly because their parents were, much less because they had the advantage of being white when building their wealth. There are of course outliers and ethnicity does have an impact, but overall there is very little social mobility anyway.
[0] https://www.goodreads.com/book/show/1842.Guns_Germs_and_Stee...