Why would they use the sperm from the "inferior" population? Because they need it.
How can they justify it? Well, humans are very good at justifying their social status while at the same time contradicting it. In the American Antebellum South, wealthy white families sometimes used black women as wet nurses, despite the prevalent ideas that a wet nurse's morality or personality could be passed on the child.
Supposedly inferior black women also raised their white employers' children. All the stated beliefs of black people (whether slaves or not) being unintelligent, immoral, even incapable of rational thought, were conveniently ignored when a white person needed free or cheap labor requiring intelligence and ethical and rational behavior.
The United States tended to follow the "one drop" rule, where children of one white and one non-white parent were considered non-white. Children resulting from (often non-consensual) unions between whites and blacks were considered black. If their mothers were slaves, then they were too, no matter what percentage of European DNA they had.
But in other countries, that wasn't always the case.
In 1931...[Neville] the official Protector of Western Australian
Aborigines...signs an order to relocate...three girls to the Moore
River Native Settlement internment camp. The children are referred to
by Neville as "half-castes", because they have one white and one
Aboriginal parent. Neville's reasoning is portrayed as: the Aboriginal
people of Australia are a danger to themselves, and the "half-castes"
must be bred out of existence. He plans to place the girls in a camp
where they, along with all half-castes of that age range, both boys
and girls, will grow up. They will then presumably become labourers
and servants to white families, regarded as a "good" situation for
them in life. Eventually if they marry, it will be to white people and
thus the Aboriginal "blood" will diminish. Rabbit Proof Fence.
Somehow, in this twisted reasoning, these "inferior" children were good enough to grow up to marry "superior" partners and have children with them. Their "bad" DNA would be diluted over the generations. But staying in their [Aboriginal] communities and not having children with white people was somehow worse?
While children of white and Aboriginal parents were treated badly by whites and considered a lower class, their children, or their grandchildren, could be white, if they looked the part.
In your world, the Utopians consider themselves genetically superior to the Wastelanders. Therefore, they believe they are entitled to take anything they need from the Wastelanders. Including their genetic material. Which is only inferior when inside an actual Wastelander. They would consider their children to be Utopians.
Don't expect logic out of bigots. It generally boils down to "I want what you've got" and "you can't have what I have." The rest is basically handwavium.