If I had a nickel for every time I suggested that race and gender discrimination are more primal than economic discrimination, I'd be one of the despised billionaires (okay, that's a little hyperbolic).

I won't repeat your arguments, since from the comments it's evident that so many people are missing the point, but I'd like to look at the psychology of the class-first argument.

Class-first (in truth, it's class-only for its adherents) provides a deterministic model (primarily for Marxism but also for non-Marxists like Bernie Sanders) that is comfortable and comforting because it is (on paper) so easy to remedy. We simply adjust the formulas, and bingo--inequality eliminated.

If you gave everyone in the world an equal amount of money / income / wealth, we would still be plagued by sexism (patriarchalism) and racism / ethnic discrimination.

Economic inequality is largely a tactic used by racists and patriarchalists (there's a lot of overlap between the two categories) for maintaining their power over others (and for indulging in the sadistic pleasure of watching The Other suffer).

There are probably a few white male billionaires who love their money so much that they don't mind if the people below them catch a few drops via trickle-down, but I don't know any of these semi-enlightened plutocrats. Their existence is strictly hypothetical as far as I'm concerned.