It was not suddenly an important issue for liberals; it was always an issue, but suddenly the protestants, who were for family planning and for use of contraception, and for abortion under certain circumstances (because they weren’t Catholics) did a sharp right turn.
Abortion was less of an issue for liberals for a long time because it was medically unsafe for a long time. It became a topic together with pills and condoms, in favour of family planning and contraception, so abortion wouldn’t be necessary for many cases.
As abortion done by doctors became medically safer than back-alley abortions or letting the pregnancy continue; and as in the 60s and 70s the next wave of feminism meant women standing up for rights to their own body, and suddenly a part of their allies turned on them, it became a battle for the “liberals” against the conservatives and the fundies.
Because “Baby-killer” for people who are pro-choice, or for women getting the Morning after-pill is a lie. And talking about “Satantic baby-killers” is also a lie made up completly. “Michelle Remembers” is not a documentary, but a lie through and through, yet enough fundies got fired up that lies about Planned Parenthood persist today.
You missed maybe the linked article. It’s not about starting with an ethical framework of doing what’s right, then looking at facts and deciding on what course achieves the best outcome.
It’s a group that thrived not on doing the right thing, but on being righteousness and telling everybody else how they were wrong, looking for a way to get on the High Horse again after being wrong, and fixing on a problem, lying about the facts, twisting established moral concepts, and the end result leading to diseases and death because e.g. conservatives have pushed through laws that make operating Planned Parenthood and safe abortion clinics difficult to impossible, leading not only again to dangerous abortions, but to many other preventable diseases being untreated (because conservatives, while claiming to care about women, don’t want to pay preventive health care for women, so PP is the only source to provide that.
But yes, both sides call names and want to be right, so it’s exactly the same. Except for how it isn’t at all.