My beliefs aside [0], you do bring up a good point. I can't find the HN thread, but there was a good TEDx presentation on it as well:

Given two curves on the same graph, you are not guaranteed to be able to min/max them simultaneously.

For example: say you are a mortgage broker at a bank and you have to give out mortgages to people in your community. Obviously, the people in your community are diverse. There are men, women, white people, black people, homosexuals, heterosexuals, etc. all wanting mortgages. Say you have some historical data that you know to be accurate, namely the credit score of successful applicants, the associated foreclosure rate, and some demographic data like race and sex. Also say that you want the bank to remain solvent and competitive, handing out loans to the best applicants and also garnering a reputation for being a 'fair' community bank that people will actually be able to get loans from. Now, the question is, what is the cutoff for credit-scores that will cause an applicant to not get a mortgage [1]?

Say, on the y-axis is the foreclosure rate, and on the x-axis is an applicant's credit score. You have some curves for white women, black women, white men, black men, and many other permutations of the human rainbow. These curves are all different from each other.

Now, if you set an arbitrary cut-off score, you may be setting a score that says that white people are less likely to get a mortgage than black people. That's obviously disenfranchising white people in your community, and you should change the cut-off to be more equitable to the people around you.

However, now that you have changed the cut-off for approval of a mortgage to be racial equitable, you have now made it such that men are less likely to get a mortgage than women are. This is also not good, and you should change the cut-off again to be fair to all sexes and genders. However, now you are back to being unfair to white people, again.

Given the data you have, you are in a situation where, no matter what you do, you are discriminatory. In fact, I'd say that this is the most likely situation to be in. That all the curves and graphs would align just so and that you could be non-discriminatory under ALL scenarios is extremely unlikely. Honestly, you do have to pick and choose who you will not discriminate against.

This may seem disheartening, and, yeah, it is [2]. However, that does not mean that we shouldn't try to change things. If anything, understanding that you will very likely be discriminatory no-matter-what, is helpful. You now have a better view of what you can change and how that may affect things. You can choose where to set your parameters with better clarity towards your fellow humans. Maybe you oscillate between gender-parity and height-parity. Maybe you choose to focus on income-inequality for 5 years and then switch to racial-inequality for a focus. Whatever your thesis is on how to gain better equity in your community, maybe you now have a better understanding of the mechanics of the system and you can better affect it positively.

[0] In talking privately to friends that are also considered 'minorities', discrimination is occurring and is systemic. Though this is personal anecdata.

[1] I'm trying to simplify this as much as possible. Obviously, real applications are VERY nuanced and complicated.

[2] Unless you are a journalist. Then, well, this means you will always have a lot to write about!