Some background information on the setting:
Religion: God is thought of to have dual sides that symbolize male and female virtues. The female portion represents logic, stability, intelligence and control. The ability to access magic was given to her as a symbol of her divine authority. She is called to lead and guide the community in the right path according to God's will. The male side represents passion, courage, honor and emotion. Men are called to protect and defend God's creation and to be its molders and shapers. Only by working together can a balanced social harmony in society be achieved.
Magic: Science and Technology revolve around magic and are used to create a form called magitech. This magic is present in all walks of society. Runes for growing crops, unlimited energy sources that power machinery, teleportals for transportation and alchemy are just some ways magitech is used in daily life. Although everyone has access to magitech, only women can access it directly and create it. Although powerful, magic is limited in significant ways. It is slow, complex and intense requiring much concentration and skill. Attack magic is a rare and specialized field.
One simple way magic is used extends to a woman's biology. All females have the natural inborn ability to control their reproductive functions. They can choose when to get pregnant and can speed up, slow down or pause the rate of gestation. Pregnancy is easy on a woman's body and children usually survive to adulthood. Women who have given birth have access to the strongest magics. Birth fundamentally changes women into a higher being, giving them a higher understanding of magic by being one with the force of creation.
Government: Matrilineal clans are controlled by a women's council with a clan matriarch serving as the head. They are primarily in charge of running businesses, banking, education, hospitals and passing laws. The clan matriarch selects a male chief who is chosen to lead an all male council. They are responsible for security, enforcement, war, defense, exploring territory and manual labor. The chief is more of a servant leader and can be removed by the matriarch if necessary. All clans make up a larger confederacy with an everqueen who is chosen by the matriarchs of each clan. Ritualized gladiator games and competitions are used to replace warfare as a means of keeping the peace between the clans.
Culture: As the bearers of life, women are viewed as the "stronger" sex as they were made in God's image. They are more emotionally stable, rational and able to cooperate to achieve long term goals. Men are valued for their physical strength, bravery and desire to protect others. These qualities make them suited to warfare which is one of the most respected occupations a man can aspire to. However, men overall can be arrogant and egotistical, sometimes allowing their emotions to get the best of them. This belief keeps them out of political power.
Children are raised communally with the clan taking part in raising the next generation. The idea of the nuclear family is nonexistent. Much of child-rearing is left to the younger women and older men. Although children normally retain close relationships with their birth mother, brothers and uncles are the main father figures in a child's life. While sex is not particularly regulated, procreation is. The creation of life is viewed as a sacred form of magic. Cooperative breeding between clans is the norm as a way of securing alliances and trade deals. These arrangements are managed by a clan breeding councils made specifically for this purpose, and are responsible for keeping records and family trees. Successful and valued men are chosen to represent their clans in this way. For women, it serves as a rite of passage and motherhood is celebrated as a high honor. For men, it serves as a symbol of their value and worth to their clan.
The world is under siege from supernatural elements from an alternate dimension that exist alongside reality. It is separated from us by a thin veil which has weakened in certain areas or completely collapsed in others, allowing the things from the other side to get through. War is fairly common with these creatures. This has influenced humanity's development and culture, and encouraged a more complementary, rigid mindset about the genders. There are those that would support more egalitarian, progressive ideas. However, with the hostile environment they tend to get lost in the noise. These people would be viewed as foolish and naive or dangerous at worst. Humanity is focused on its continued survival and that tends to be prioritized over individual liberty or civil rights.
Given the setting, would magical birth control in these circumstances give rise to a rigid, conformist, and controlled society?