Abortion reduction, a la Ryan-DeLauro, is supposed to solve this problem by taking abortion off the table, but of course, that's not the way it works. As with other memes, the more you repeat the frame, the more power it has.
I realize that obviously these questions are not going to go away any time soon. Nor can we reasonably expect people to deny their beliefs, whatever they may be. The optimal situation is probably to break the link between "people of faith" and opposition to reproductive rights, so that the knee-jerk reaction to talking about faith in the public square isn't immediately to ask about How It Affects The Abortion Problem.
How that can be done, I do not know. I suspect, however, that it will wind up looking a lot like the recent moves of the ELCA and ECUSA to liberalize on the question of gays and lesbians in the church: some of us is fer it, some agin, now can we please move on