Now that some states are mandating birth (there's no other term for it), they're going to fall back on the moral/social principle of "individual responsibility." We already know that, if conservatives have their way, they will cut aid to poor families, which are mostly headed by single mothers. There will be an increase in the number of poor, mostly-single mothers.
If I would put myself in the head of an Anti-choicer, I would say that this is a necessary evil for preventing the killing of children (fetuses), containing, if not stopping sin, and perhaps keeping God from getting angry and smiting our great nation, the way he did Sodom and Gomorrah and all other wicked nations in the Old Testament. The fact that this is oppressive to women is just the lesser of two evils, or at worst, a distraction from what's really important.
You see, since the Yahweh in the Old Testament destroys whole nations for their sins, if you're a fundamentalist or near fundamentalist male, abortion becomes the business for you and everybody, not just for the woman and her doctor. If abortion is illegal, and a woman has an illegal abortion, then she, her doctor, and possibly her sex partner have sinned. They've murdered, and she has possibly sinned sexual. But the sin stops there.
However, if the US has legal abortion, then, as a fundamentalist sees it, the whole nation is sinning, and is in danger of God's wrath, either in the world or the afterlife.
Now, to be fair, they would also say the man should marry the woman and help raise the child, which means making an awful marriage, oppressive to the woman, and in an economic system where a youth can no longer count on getting a job without an education. If he does get one, his family needs two paychecks at the pay-rate of unskilled jobs, and it's still probably not sufficient. It's no longer like the fifties where you could have shotgun marriage and husband could, perhaps, get employment to meet his responsibilities. Also, of course, if the father can't or won't meet his family obligations, then the mother is the person of last resort for the children. It's not exactly true that a man abandoning a woman can get away scot-free especially with DNA testing. But even if he pays and works, that still leaves her with the day-to-day care.
The "coincidence" that this whole set of social-religious beliefs support a system that is oppressive to women is off-topic for them. "Just a necessary evil." There's no use in pointing it out to them.