Although the Catholic Church as an institution is strongly pro-life, I don't have knowledge of its direct involvement with CPCs. Others on this forum can probably speak to that issue.
Many of the Protestant churches are wolves in sheep's clothing. They're as pro-abortion as they are theologically apostate. There'll be freeze warnings in the eternal habitation of the unredeemed before you'll see them trying to save babies' lives.
I seriously doubt that any of the Protestant churches is in FAVOR of abortion, but it seems to me likely that the tactics of some pro-lifers have put them off. You have to admit that there are reasons why many respectable organizations want nothing to do with the pro-life people. The pro-life movement needs to clean it's own house before it will become widely respected as a serious, responsible movement.