The key word among liberal Protestants probably is freedom. They feel free to make up their own minds. I know of one Protestant family, for example, in which the wife had an abortion after giving birth to four children. Why? The wife had developed major medical problems and the doctor warned her that another pregnancy could kill her and the baby. There also was the economic crunch. They decided they wanted to give the four the best in education and that more childen would make that less likely.
I know of another Protestant couple where the wife had been raped as a teenager, and she had had an abortion well before their marriage. And in another instance a downs syndrome teen had been gang-raped, became pregnant, and the parents decided that an abortion was the only way of avoiding a myriad of serious problems that would continue for many years. They felt assured that the fetus, if truly a baby (there is debate among many, of course, as to when a fetus becomes a baby), would go directly to heaven "and may actually be better off than the rest of us" - quoting the Dad as he sought to justify the abortion.
What troubles many Protestants about the Catholic position is that its opposition to all abortions is paired with its sharp condemnation of all birth control except the church-approved variety, which can seem unnatural in a happy marriage relationship but also is not very reliable.
What many Catholics may overlook is the Church's position on abortion seems ineffective. Statistics that are available suggest that abortions are as common among Catholics as non-Catholics.
Off topic a bit, but I recently saw a Pew poll which asked four groups how they felt about same-sexual marriage. Mainline Protestants opposed it by a narrow margim - roughly 46% against, 43% for, or some such figure. Evangelical Protestants and Black Protestants both were heavily against it. Only Catholics favored it, by a small margin, something like 45% for, 42% against. That seems to say something about the way in which millions of Catholics regard the mandates of the Church
. I suspect this refers to abortion as well. Many Catholics apparently feel that abortions should be very rare and very safe, but should be permitted with certain restrictions that some states have imposed - e. g., notification of parents when a teenager is involved, showing a film of an embyro in the womb, requiring a time for reconsideration before an abortion is performed, etc.