Both can then hopefully direct their efforts towards the real problem, need for abortion. If that can be reduced or even eliminated with more support and sex ed, both win. Maybe not in absolute terms, but it's something.
This might not always be possible for disagreements, but sometimes it can help to step back and consider the issue and it's implications for society from other angles.
A pro-life person could say, "I believe that life begins at conception (or when the heart starts, or when the brainwaves start), and after that, abortion is murder. But I also understand what a horrible position that puts many women in, and the real pain it causes in real lives. I still can't compromise - I believe abortion should be illegal - but I can understand why people are on the other side, and I don't hate them for being there."
And a pro-choice person could say, "I care about womens' ability to choose what they want for their own lives. But I can see how, if you genuinely believe that abortion is murder, you simply can't support it in good conscience. I can't agree with you, and we can't compromise. But I can respect you for standing for what you think is morally right, even when I think you're wrong on what is actually moral in this situation."
Wouldn't that be better? It's still an unresolvable issue. But if we could remove the hatred on both sides, wouldn't that be better?