I'd argue both are unrelated to outlawing abortion.

There may be people who want to ban abortion because they just want to control women, but my moment was seeing my 10 weeks in gestation son kicking on the ultrasound. I saw this human with arms and legs moving around on its own, and I watched that little human and watched his beating heart and the thought that popped in my head was a sardonic "it's just a clump of cells" -- it clearly wasn't just a clump of cells. That was a tiny living human. Wilfully killing such a thing because it's inconvenient or defenseless or because you can't see it since it's behind a layer of skin didn't seem acceptable at that point. My right to swing my fist ends before it hits your face.

On a completely different track, historically there are examples where different cultural values led to completely different outcomes. For example, in imperial Japan, babies weren't considered people at all and children came to exist in the real world on a spectrum as they aged, so there was an extremely common practice of killing babies when they were born for the good of the community. In one famous story, a person who was considered moral had a relatively grown child and his mother, but not enough food to feed both, and killed the child so the mother could eat and that was considered just because the mother could have more children in the future. That goes to show that changes in underlying cultural assumptions does make a big difference in the outcomes of the moral calculus.

That being the case, we reach an ought-is problem. We can largely agree on the objective facts, but our interpretation of those facts, and the principles upon which the facts are judged against change, and so similarly two people in the same society can come to wildly different conclusions. In my case, I spent 12 years trying to have a child fully ready to have one, finally succeeded, and raising my son is one of the most deeply existentially fulfilling experiences I've ever had. Of course I'll come to much different conclusions than someone who doesn't want a child, can't support a child, is sure they'd be miserable if they had a child, and has no idea what that baby looks like.

It's important to realize that just because you deeply disagree with someone doesn't mean they're necessarily evil people. The moment you start dehumanizing people by making them into the personification of evil, that's actually when you start seeing things like the Nazis because when you're fighting pure evil the ends always justify the means.