I actually wrote about this as part of my Masters thesis (which was about portrayals of anti-abortion violence on TV, but the history of the anti-abortion movement was relevant).
It's been a few years and I'm not currently looking at my Masters thesis, so I'm not going to cite any sources off the top of my head, but there are actually a few really interesting points that happened in the anti-abortion movement.
There has actually been an active anti-abortion movement since at least the 1800s in the US. Its shape and motivations have gone through a number of changes across the years, but it's definitely been there.
First, Catholics have basically always (at least in the US) been anti-abortion as part of a broader pro-life effort (anti-death penalty, anti-war, pro-charity, etc.) because they have basically always seen life as beginning at conception. This is not a defense of the Catholic Church or the Catholic anti-abortion movement, but it has historically been pretty distinct from the more modern evangelical anti-abortion movement. Ironically, the modern shift towards evangelical/Republican anti-abortion politics pulled Catholics writ large away from as much active anti-abortion campaigning, because they didn't want to be associated with the evangelical part of the movement.
A lot of early (late 1800s/early 1900s) non-Catholic anti-abortion stuff was about race and immigration--namely, the fear that white Protestant women weren't having enough children and so white Protestants were going to be outpaced by POC and Catholics who had a lot more children. Sound familiar?
Before Roe, abortion was largely seen as a medical procedure. It was a highly and inconsistently regulated one, but it was a medical procedure, and so most mainstream Protestants were cool with it because it wasn't seen as anything beyond that.
A few things happened at around the same time: the growth of the evangelical movement, which strongly opposed feminism and anything that was seen as not fitting the extremely patriarchal hierarchy wherein the father is the head of household and the center of life and women's job is primarily as a mother and a wife first, the passage of Roe, and the Republican effort to grow their base.
A lot of the evangelical part was about race, but you shouldn't discount how much evangelicals fundamentally believe in the anti-abortion movement. They just haven't necessarily always fully believed in it as a "life begins at conception" piece--but the belief that women are first and foremost a mother and anything that prevents them from being in that role is evil is really fundamental.*
But the passage of Roe is that it changed abortion from being seen as basically just a medical procedure to "abortion on demand." Now it wasn't just to save a woman's life or because the fetus wouldn't survive--it was being a woman didn't want to carry a child. Suddenly it was this idea that a woman could (and would) use abortion as birth control, that they would have random irresponsible sex and then get rid of children willy-nilly.
This ran headlong into the swiftly-growing evangelical movement and helped lead to the modern anti-abortion movement.
*You can look up stuff about women-protective/women-centered vs fetus-protective/fetus-centered anti-abortion beliefs. Most of what I read for my Masters is paywalled but you can find some of it online.
