Whenever one finds a "dissident" group that appears to advocate for the exact opposite of what an organization generally stands for, it's a good bet that it is insincere. Choose your term of art - "astroturf", "false flag" - the notion is that it's basically a front group that's trying to attack the organization from within.
In the realm of religion this is a bit strange because (especially in the United States), there are few obstacles preventing movement from one belief to another. Obviously, people in concentrated and close-knit communities such as the Amish or Mormons might find support "on the outside" hard to manage, but if one deeply disagrees with the teachings of the faith to the point of openly disputing them, that decisions has already been made.
There are of course a few exceptions where the dissenters actual win. The Anglican Church is one example of this. Just about everything the Anglicans believed in a century ago has been discarded. Heck, the changes over the last 25 years have been profound. So it is with the United Methodists (which are in fact breaking up) and other Protestant groups.
Within the Catholic Church, however, such movements gain little official traction. In fact, right now the Church is seeing a strong push from the laity to become more orthodox, more faithful and more consistent in enforcing doctrine. The current moral laxity (such as that originating in Germany) seems to come entirely from the leadership, which is stuck in a 1970s mindset).
Thus we have the strange creature known as the "pro-choice Catholic," an individual who claims to be a member of the Body of Christ, yet for some reason directly contradicts sacred scripture, Church tradition, long-standing doctrine and Papal pronouncements.
As my father likes to joke, there's a term for people like this: "Protestant."
I think the issue is twofold. On the one hand, there is the egotism of thinking oneself smarter than the Church fathers, the Magisterium and the rest of the faith. For some odd reason, people sometimes produce polls showing that a significant amount of Americans support some form of abortion, as if the Catholic Church is some sort of elective body.
There's also the fact that these people tend to be older, cradle Catholics whose identity was shaped when being Catholic was more of an ethnic identity than a religious one. Neighborhoods were more ethnically homogeneous, so on Sunday, all the Irish, Italians, Polish, etc. went to Mass by default.
These communities have broken up over time, so there's no comparable social pressure. Catholics are fully in the American mainstream and have been for a while. Still, the older sort clings to their nominal faith perhaps out of a nostalgic sense of victimhood.
In any event, I think there's another aspect to this, which also is rooted in the past, and that's the experience of socially ambitious Catholic women.
Young women in the 1960s did not have a lot of options for birth control. Yes, The Pill burst on the scene (with disastrous results), but women of "good character" would never admit to taking it. Certainly not Catholic girls.
Similarly, the time-tested condom was out of the question. For one thing, "nice girls" didn't dare keep them around, nor would they admit having planned to have sex outside of marriage.
This is why abortion became such a lightning rod - because these women were going off to college, experimenting with relationships and wanting to try sex - but if they got pregnant, their lives would be completely ruined.
None of them could face the disgrace of being an unwed mother. To them, it was worse than death, a live without the dream of house, husband and children and the social stigma was too terrible to contemplate.
Adoption was not really an option because it would require months of seclusion and also a paper trail. Even if all went well, the child might come back, and could wreck an otherwise happy marriage by exposing Mom's Dark Secret.
Abortion avoided both problems. The baby was obliterated and no one would ever know. Having made "a mistake" the woman could resume her hope for a nice husband and happy home - and children whose entry into the world would bring her status rather than shame.
I think this attitude is pervasive among women over 50. Under that, it's more of a tribal membership because by the time the Gen Xers were getting into college, condoms were pretty much being distributed far and wide. Birth control had lost its stigma even among Catholics, and if one didn't want The Pill, there were other more discrete but effective options.
But for the generations before, abortion was the only option. "Nice girls" didn't keep that stuff lying around and in fact if - at the moment of decision it was produced - the man might be filled with disgust. Here he thought he had truly seduced the innocent, only to find out he's bagged a slut with a condom stash!
To be clear, none of these women necessarily wanted pre-marital sex, but if they got lost in the moment, what would be their recourse? Abortion would.
Of course, the world has changed considerably since then. There is zero stigma in popular society to pre-marital sex or using birth control. Religious communities still frown on it, but they're also strongly pro-life.
In that sense, the secular victory in the culture wars over sexual preference and promiscuity are the very things destroying the necessity for abortion. Given the many, inexpensive and reinforcing methods of birth control that are available, there is simply no reason for the procedure other than the three classic exceptions: rape, incest, and life of the mother.
But for people stuck in the past, none of that matters - they're still fighting the battles of their distant youth.
Which is odd, given that so many of them identify as "progressive."