I've noted before that you can generally group ethical approaches on the basis of whether they treat consequence-based reasoning, obligation-based reasoning, or character-based reasoning as fundamental -- an ethical approach could use any and all of the three, but maintaining consistency generally requires treating one as more direct and definitive than the others. This is not a mere matter of classification; it has some practical relevance.
In the United States, our discourse and vocabulary for handling ethical issues concerned with racism has historically shown a clear and obvious deontological bent, treating obligations and rights as fundamental. This is largely due to the fact that most of the major and influential figures in the Civil Rights Movement, despite their many differences from each other, tended to frame their own work in deontological terms. The resulting vocabulary is a bit mixed -- it doesn't descend from a single kind of deontology -- but it clearly suggests both a deontological understanding of racism and a deontological approach to addressing it: human and natural rights, dignity, a focus on intent, an emphasis on the importance of coming up with rules and guidelines that everyone in every circumstance can follow to fulfill their duties to each other.
However, the U.S. (and much of the West) has a culture that naturally tends consequentialist. It's a future-looking culture that emphasizes choice, harms and benefits, and consumption measured by satisfaction and dissatisfaction. In the U.S., even people who are definitely not consequentialist will tend to slip into consequentialist-sounding ways of describing ethical situations, and consequence-based arguments in practice tend to serve as a lowest common denominator for everyone: when people find themselves in apparently intractable arguments, they tend to shift to talking in terms of consequences on the assumption that this will make more sense to their interlocutors than whatever the arguments were in which the discussion getting bogged down. Perhaps unsurprisingly, then, we have seen an increasing tendency to talk about ethical issues of race in consequence-based terms. This is clearly what is behind a lot of the increasing emphasis on 'systemic racism', which in practice tends to be defined in terms of harms and lack of benefits. Likewise, it's clearly involved in the usual 'equity, not equality' slogans, when you press people to explain what they mean. It's also seen in the revolt -- sometimes quite intense -- against focusing on intent in the traditional Civil Rights manner. Perhaps the most obvious example of the attempt by consequentialists to seize the discourse on race from the deontologists is the tendency to hold that 'color blindness' is itself racist. From the traditional deontological perspective, this is obvious insanity -- even if you wish to qualify it (and some would), it is the right kind of thing to aim at when you are interested in upholding standards that apply the same to everyone and treat each person simply as a person, a decent first approximation of how to oppose racism. But it's obvious why a consequentialist would want to get rid of it: 'color blindness' will directly block most consequence-based reasoning about racial issues, and those kinds of consequence-based reasoning it lets pass it will subordinate entirely to a focus on intentional treatment of others. Likewise, the practical approaches consequentialists often prefer instead of color-blind rules have many of the features that deontologists have historically seen as associated with racism.
When deontologists argue with consequentialists about racism, there is no direct reconciliation; the fundamental accounts of the central issue will differ in such a way that the two sides will inevitably be using terms differently. And since both sides tend to regard this is an area of life filled with non-negotiables, the argument is not going anywhere.
Of course, this is complicated by the fact that neither consequentialism nor deontology is the right approach to ethics! But character-based approaches are mostly minor players in our current disputes.
