...which is exactly the kind of "treating culturally- and situationally-contextual results like inherent facts" bias the article is talking about.
Honestly, my preferred method of solving this would be to train the algorithm on a data set with all of the forbidden values included along with anything else the creator feels relevant - zip code, income, familial status, favorite sport, education - and then when running in production, against real people, don't give it the restricted information. Yes, you could theoretically extract race, gender and other protected stats from the information the algorithm actually uses in prod - but it has no incentive to, since a less-noisy signal is already provided.
For instance, suppose the optimal algorithm for your data set is some linear function of X, Y and Z - let's say X+Y+Z to keep things simple. X,Y and Z are all normally distributed variables, mean of 0 and the same standard deviation. Y has a 0.5 correlation with X, and a -0.5 correlation with Z. If not provided Y, your algorithm might come up with 1.5X+0.5Z as an approximation - extracting a bit of the signal for Y from the things it does have access to. It's suboptimal, but better than just X+Z. Unfortunately, Y is verboten - we're not allowed to discriminate on it, and this approximation ends up with results that track Y. So instead we train with X, Y and Z as inputs, so the derived model is X+Y+Z - and we can drop Y from that model in production, leading to a model that (while less accurate) shouldn't unfairly track Y.
The problem is that the output of those algorithms is used to drive decision making that has the effect of maintaining the status quo, by removing opportunities to change it.
The whole point of using the algorithm was to make sure personal biases aren't impacting the decision. If we're going to alter the algorithm because we don't like the result, then why are we bothering to use an algorithm in the first place? Just use a human to make the decision. At least in that scenario potential biases have an identifiable source, as opposed to an opaque program that may have been made by engineers that deliberately tuned it to avoid any disparities because they think any disparity in outcome is fundamentally problematic
I think your comment shows that you understand this. You accept that a decision may be correct, when measured in totally cold and statistical terms. But such decisions would not "change the status quo" and that would be a problem.
But that position is a deeply political one. Why should decisions at banks, tech firms, or wherever be deliberately biased to change the status quo? It's social engineering, a field with a long and terrible track record of catastrophic failure. Failure both to actually change reality, and failure in terms of the resulting human cost.
Injecting bias into otherwise unbiased decisions by manipulating ML models, or by manipulating people (threatening them if they don't toe the line), is never a good thing.