In this question, I detail a world with a third human sex, lilim, who have bat-like wings and taloned feet like a bird's. The TL;DR is that lilim give birth to equal numbers of men, women and lilim (and early-miscarried male lilim), while women give birth to only men and women. Lilim are a female sex.
The issue is that given that lilim have slightly lower birth rate than women, and only 1 in 3 births is a lilim and 1 in 3 is a woman, while half of the offspring of women are women. Going by pure genetics without considering selection pressures, lilim are doomed to becoming extinct or a minority curiosity.
An additional complication is that until the age of between 6 and 9, a woman-child and a lilim-child are indistinguishable.
However, lilim aren't willing to just sit back and let that happen. On the world to which lilim fled after it became apparent that their sex would become extinct on our own world, there was a war between the Vilifiers - lilim who vilify women and advocate preventing them from reproducing, and the Nurturers, who couldn't stomach the wholesale sterilization and/or murder of a third of the population. The result of the war was that the population separated, with the Vilifiers on the original world and the Nurturers on a new world.
I'm sure that we can imagine the sorts of atrocities that a people at war with their own genetics could perpetrate. However, I'm interested in more subtle methods of controlling the population of women that the Nurturers might practise. The Nurturers are still lilim, and are still not willing to allow their sex to become extinct, they just have more scruples.
So, the question: How might lilim reduce the rate at which their woman-children reproduce without denying them the opportunity to reproduce at all, with the most effective and least intrusive, cruel or obvious methods being preferable.
Religious solutions are not acceptable. Their society rejected religion at a particular point in their history prior to the Vilifier/Nurturer schism. I'm looking primarily for psychological, sociological and legal solutions.
Technological, magical, surgical or pharmaceutical solutions are also out unless the women voluntarily have themselves sterilized or use birth control, the Nurturers feel that such solutions are a step too close to the practises of the Vilifiers. Any such solution must be voluntary and not coerced at a personal level.
The lilim understand Mendelian genetics, but are not capable of genetic engineering.
To bring the genetics in from the linked question, men have X and Y chromosomes. Women have XX. Lilim have LX. LY male lilim offspring do not implant into the uterus, and so is lethal. Viable LXY male lilim occasionally occur, but are not genetically significant, as they are sterile.
Also, for the sake of evolutionary history, before Adam meddled, Women had WW chromosomes, men were WY and Lilim were WL. LY was still lethal, as were WW women-children when they were carried by lilim. Women became extinct due in part to the higher survivability of lilim. Then Adam changed the W chromosome in men to X, and added selection pressures which led to the elimination of the unmodified W chromosome.