"For example: let's agree for the sake of argument that a newborn has moral rights, and that gametes do not. It doesn't make much sense to give the fetus moral rights only based on its physical location, therefore at some point between conception and birth the fetus gains moral rights. No matter what point n we choose, the objection "why is one day earlier any better" seems pretty persuasive. Therefore, by induction, the only point for assigning rights which can't be argued against in that way is at conception. Thus, we should disallow abortion so we aren't depriving the fetus of its rights."

That's roughly my position, as an atheist libertarian. although I don't back it up all the way to conception, just to a point in early pregnancy where it seems overwhelmingly clear the fetus has no attributes which could reasonably demand respect for rights.

Abortion has been conflated with feminism, like how, say, tariffs are conflated with Republicans right now, but there's no ideological necessity for that. Just cultural trends.