Discrimination does not have in itself any moral value. I can discriminate my left hand from my right hand... So what?
I expect that we can all discriminate between White and Black people, between tall and short people, between friendly people and irascible people, between Leftists and Rightists, between intelligent and stupid. So we do make a very large number of discriminations and this self-evidently raises no ethical question whatsoever.
That being said, discrimination is often used to restrict certain rights to certain people or inflict unfair treatment on others. In such cases, the unfairness is entirely in what discrimination is used to achieve, not in the discrimination itself.
The argument put forward in the question is entirely fallacious as it rests entirely on the equivocation between two very different senses (2 and 3 bellow) of the word "discrimination":
The ability or power to see or make fine distinctions; discernment.
Treatment or consideration based on class or category, such as race or gender, rather than individual merit; partiality or prejudice.
Everything we do in life requires us to make fine distinctions and so to discriminate between things that are effectively different. Governing a country also requires that ministers and administrations make fine distinctions, between mothers and children, between workers and retirees, between foreigners and nationals, etc. This is absolutely necessary. This is at the foundation of life itself. There would be no effective action possible without discrimination. Life itself would be impossible.
The problem only starts when discrimination in sense 2 is used to discriminate in sense 3: use the different colours of the skin of people to restrict certain services to White people for example, services such as certain buses, certain schools, certain jobs. Discrimination in this sense can be overt and assumed, as it was in South-Africa at the time of the Apartheid, or in the United States of America not so long ago, or more discrete, often to the point of hypocrisy. So much so that there is probably no society on the surface of the Earth which free of unfair discriminations.
The point I am making here is completely obvious and should go without saying. The question asks "if anyone attempted to justify this apparent contradiction from a moral philosophy standpoint". This is the wrong question. The question should be how can anyone justify any unfair discrimination? And unfortunately, the question itself is an effort to do exactly that using a fallacious opposition based on equivocation. Moral standpoint?