If the algorithm charges higher car insurances premium to men, does it mean it is fair?
You have a choice of whether or not you believe being male causes car insurance claims. That is independent of the statistical correlations. Ten times a day people say correlation is not causation, but a hundred times a day, I see people implicitly insisting that it necessarily is.
If I'm running an insurance agency and not a public policy advocacy, and my data keeps showing that men have higher accident rate than women, I can just ignore causation and build my actuarial tables based on that. I don't need a casual model here, at least not until the point I'd want to optimize my models further still, but there are diminishing returns on that.
Suppose (just as a toy example) that being young causes accidents, and the population of men is younger, but being male does not cause accidents. You are going to charge mature men too much and lose that business to a competitor with a correct causal model.
This is quite separate from the correlational data.
The insight I get from the article is that the "correctness" of your causal model can incorporate social justice or political correctness, without being objectively mistaken, because causation is not defined by measured correlations.
The reason fairness has so much headway among engineers isn't just an aversion towards discrimination among educated people. It's that we all know this stuff is way jankier than we care to ever admit, and that we'd never want to be the data sausage going through the algorithm grinder.