So you are arguing that one absolutely cannot force or deny a medical procedure or medication (including both because abortion by drug is the most common) on another person because to do so is a violation of their bodily autonomy? There are a lot of anti-science and anti-vax idiots that agree with you, they just want that reasoning to apply to things that aren't abortion. Nobody is consistent about the bodily autonomy argument, and a belief in medical bodily autonomy that hinges on what specific procedure we're talking about is fundamentally hypocritical.
Well Doctors can and do refuse to preform medical procedures all the time. Doctors have a duty of care, sure, but you can't like schedule a surgeon to remove your legs just 'cause.
The distinction is the legality of it. Of governments passing laws forbidding medical procedures, especially when the termination of a pregnancy would save the mother's life, or the fetus is no longer viable/wont survive birth/childhood.
In terms of vaccine mandates, I'm actually against mandates per se. The government shouldn't be able to force you to get the vaccine. However it has every right to impose mandatory vaccines for certain sociality actions. No vaccine? Sure. You can't go to public school, or go to public events, use public transportation, travel on public roads or internationally travel. Hell I would go one step further and say you can't use government emergency first responders. No vaccine? That is your right, and you may put yourself at risk of a disease. But you don't have the right to put firefighters at risk.
And I hold the same for churches. Don't pay taxes, don't get ambulances.
There is a social contract and you either agree to it, or don't. Both are acceptable, both have consequences.
I could apply exactly the same logic to child support. But if I were to say that "Men are not slaves to women, and no woman has the right to force a man to do something he doesn't want to. Any other discussion is just trying to hide slavery by another name." in that sort of context (where it's literally about (typically) men's labor being exploited for (typically) women's benefit based on something he has no control of whatsoever beyond "don't have sex") it definitely wouldn't fly, though. Apparently it only counts as slavery when the labor is biological in nature?
There are actually ways to get out of child support, and there are cases of women like raping men, getting pregnant and being denied child support. And if I recall correctly, a father can "abandon" the child, not sure what the legal term is, and say not his, he wants no part in anything to do with it, and doesn't have to pay child support.
Also women are increasingly being forced to pay child support when they're not the primary parent, so yeah gender equality.