Sadly, in a polity like that, the "donations from unfavored half", if they refused to "donate" would likely then be forcefully rounded up, thrown into chains, and dragged to "camps for their own safety", at least that would be the spin. There their "betters" would likely try to forcefully take the eggs, unless the treatment in question removed the ability to make the eggs. Then I can see them trying to go out and kidnap females from other worlds, and end up facing Pax Humais form of "justice".