But, you realize it's largely a question of axioms, right? Two sides are talking past each other because they take their axioms for granted as self-evident.

It's simply a question of a woman's reproductive rights if you take it as axiomatic that a fetus isn't a person.

I don't take it as axiomatic that personhood begins at conception, but if I did, it would all of a sudden be a question of balancing the rights of two people instead of just the woman's reproductive rights. We don't have a clean scientific definition of personhood. The fetus is genetically distinct and is essentially a parasitic larval human. Scientifically, it's just tissue, but so am I. The real question is if it's a person, and that's a legal and moral question that is largely axiomatic.

The reality is that very few of us have a problem with aborting an unviable fetus or early abortion in cases of rape, very few of us support aborting a perfectly healthy fetus minutes before birth, and hard science doesn't provide us many clear lines somewhere in the middle.