There is no necessity for denigration based on race for anyone.
It's a deeply implanted and very unfortunate aspect of U.S. culture that has only been working its way out for the past sixty years or so. There's still some left, though a lot is gone; a few patches are strengthening regardless. People with your attitude are the second greatest cause for the strengthening. (#1 is Patriot Front types.)
It's historically true that when our idea of equal opportunity was conceived (that is, the idea that is the intellectual and legal heir--the idea has been expressed throughout history and across the globe), it was conceived by white people for white people. That there was absolutely nothing whatsoever about it that depended on white skin did occur to a lot of people, white and otherwise, and this idea has been the source of basically every advancement of racial rights and justice throughout the entire history of the United States. This is the intellectual engine behind even conceiving of the changes as justice. So I'm assuming that if you're arguing with individuality, you're arguing with it on a very, very limited basis.
Instead, I'll interpret it as you arguing with the implementation of individuality as "whites receive it because they oppress others".
First, let's clear up that this is--as a logical necessity--completely absurd. If everyone suddenly turns purple and develops amnesia about their race, nothing changes except people commit their microaggressions based on gender and age and so on instead. Everyone has to treat everyone else as an individual and...that's...totally fine. They can. White people treat white people in 99% white areas with the same kind of equality that happens in other areas.
So I'm assuming that you're not making a logical argument. Perhaps instead you're making an economic argument that the necessary resources to engage in the luxury of treating everyone as individuals is present in society only because of the effort of oppressed races.
So, let's do a thought experiment. Let's suppose, right now, BAM, instant equality. Everyone suddenly gets the exact same income distribution as white people, except uniformly scaled down so that the GDP is unchanged. We won't worry about education or skills or anything--just somehow magically this happens.
Now, the hard part: let's take those people who are deprived so can't be afforded individuality. Pick an income level--any one you like, for the purposes of the argument. Below that, you don't get individuality. Above that, you do. Calculate what fraction of white people who used to fall above that cutoff now--with complete pay equity--now fall below.
(Cheat code: just say "calc", pick a number and ask me and I'll do the calculation for you, showing my work so you can verify.)
Doesn't this number seem awfully small to justify your complete generalization across race?
If it doesn't work like this, how does it work, mechanistically? Peter sees Hunter and says hi; and Peter sees Don and says hi; and Peter sees Charles and says hi...but somehow Peter necessarily can treat only one of these people as individuals?
So, finally, maybe you're making the social argument that without an outgroup to vilify, people can't come together enough to treat each other as equals. If this is your position I can't argue very strongly against it because the historical precedent is limited but (1) it's been going the right direction for most of the past 60 years so empirically it seems wrong, (2) why on earth are you pulling in the direction to exacerbate the outgroup effect--it seems completely counterproductive unless there is literally no distinction in level of oppression caused by this effect--it's already maxed out. (Then one would need to explain if it's maxed out, why the 50s were apparently worse.), and (3) if it's true then Amy Wax was either oppressed (in which case your argument against her was senseless) or was part of the group where individuality works in which case there's at least the possibility of considering her as an individual so criticizing her on individual merit makes sense and if that makes sense so does actually checking merit.
So, any way you slice the argument--using reason rather than prejudice--it fails badly.
It kinda sorta worked as an argument in Zimbabwe in the early 60s (or 1920s for that matter). Really doesn't seem compelling today.
And anyway, your argument is all an aside. It's an interesting aside, and tangentially relevant, and apparently deeply prejudiced, which is why I've responded. But it's an aside.
The bottom line is whether or not it is fair to disparage Amy Wax as undeservedly holding her position. You provided no justification for that. You only talked about the other direction!
So--still bigotry! Still bad. Person doing it--still deservedly reprimanded.