You know, women who are conservatibe or against abortion are also allowed to object to their children being abused by the medical system. And they don't have to shut up about their other political views to be heard about it.
But I really wonder - Do you understand that the issue is not actually access to things like contraception - it is access without the knowledge of the parents.
You can make exactly the mirror image of the argument you have made. Girls who are being abused and exploited aren't picked up, even when they are underage, because doctors provide them contraception and abortion without much questioning, and the parents have no idea what is going on. The medical system is essentially enabling these girls being sexually exploited and cutting their parents, who are the ones who care about them most and know what their lives are like, out of the picture. Unlike doctors who just get the story the girl tells them and often aren't in a position to question it. Or in some cases just believe they have to let the kids do whatever they want and provide contraception because there is no point is trying to stop them from getting into bad situations. (This is where some of the contributing attitudes to the grooming gang stuff in the medical field comes from, IMO. It's totally embedded in the normal way girls sexual health is managed.)
This scenario isn't a fantasy, it's pretty common, and actually I think something feminists ought to be pretty concerned about. Recent events with gender ideology perhaps makes some of the ideas many feminists assumed were solid, about removing parental oversight in teenagers, on less sure ground. They did, after all, come out of a period that could be rather blase and permissive about the possibility of young girls being sexually exploited. There is nothing wrong with reconsidering this sort of thing.