" . . . a poll commissioned by The Washington Post and ABC . . ."
First, it's a bogus poll.
If you're talking about "Catholics" who were baptized as infants and at best show up for Mass at Christmas and Easter, the poll would be the same as one that reflects the population as a whole and the population as a whole don't support abortion "in most if not all" cases.
People who do show up for Mass on a regular basis have been the backbone of the pro-life movement ever since Roe. They're responsible for keeping the issue in front of the public for so long that we finally have a majority who agree that abortion has to be regulated and limited to some extent and faithful Catholics are still the backbone of the pro-life movement.
I blame people who go along to get along for their own actions. What the parish priest or the bishop does isn't a major concern to such folks. Whether they claim to be Catholic or they claim to be something else, their real religion is American culture. Whatever becomes the majority view most folks find a way to adjust their "Christian" faith to accommodate the changes.
Going along to get along is such a powerful meme that even supposedly conservative "Bible believing" Evangelicals have reversed what they teach about divorce and contraception and now accept both. Once you embrace infanticide as no worse than speeding, embracing everything else is easy. The majority of people who claim to be Catholic accept contraception just like the majority of other folks who claim to be Christian and if a priest or pastor preaches that something they accept is wrong they'll just go elsewhere.
The only difference between Catholics and other Christians is that someone who claims to be Catholic is measured against the standards of the One, Holy, Catholic, and Apostolic Church Jesus Christ Himself established. Non-Catholic folks, on the other hand, measure themselves by the standards of whichever of the tens of thousands of groups they claim to agree with at the moment. Those who claim they're not a part of any organized church only be compare themselves to their Self Alone because the only standard they have is their Most High and Holy Self, the least demanding standard of all.
As for Bishops and Priests, there has never been a shortage of "shepherds", Catholic or anything else, who test the wind and then give the people in the pews exactly what they want to hear. That's how clergy who want to go along to get along behave. If the parents of the people in the pews had made sure their children knew the One True Faith there's a good chance the majority would demand that their priests and bishops stick to the high standards of the One True Church.
People in leadership roles who are actually leaders have always been scarce in most fields. Among clergy they're probably even more scarce than elsewhere and without leaders who stand their ground very few folks will. When real leaders who stand their ground rise to the top, more lower ranks will stand their ground rather than going with the herd. Until then, most Catholic parishes will be just like most non-Catholic congregations and have priests who give the congregation exactly what the majority want.
I have felt that this goes back to 1929-1930 Lambeth conference when the Church of England decided to accept artificial contraception. The minute you see life as an inconvenience you open the door for a myriad of sins.