This is a very interesting reply.
My first reaction was, how about the Catholic church giving up their opposition to birth control?
If we assume honesty on both sides (Hahaha) maybe we could agree on some basic idea. That could be that both sides prefer abortion not to happen. The pro-life side is clear on this, and don't the pro-choice people prefer that nobody needs an abortion because all pregnancies are desired? That could lead to a common effort to make contraception better and more available, involving some research, maybe free contraceptives and lots of education. That way the two sides could unite, in at least one area.
Yes, I know that's unlikely, not least because the religious right are really against sex itself, not contraception.