Eh, perhaps I'm cynical, but listening to someone, and coming to understanding regarding how they might have developed there beliefs, sounds nice, and it's very compassionate, but I question if it's actually a step toward compromise, or simply understanding. After all, for an increasing number of issues, in the end, the beliefs themselves are so polarized they leave no room for compromise. To this woman, it doesn't m…
You're probably able to use a technical definition of "belief" along the lines of "falsifiable assertation". Most people don't see it that way; being conditioned to equate "belief" with "opinion that is factually wrong". Even for those of us that know the technical definition, we have to make a conscious effort to no fall back to the casual definion on our day to day lives. And from there, there's a slipery slope that goes down to "opinion I do not agree with".
It is much more productive to see this issue in terms of values. If is not that this person cannot see the facts, but that she assigns a moral meaning to those same facts that is different from the one you would prefer.
From there, it is Politics 101. If you want her to withdraw her opposition to abortion, you have to find some other issue X that is of comparable value to her, and either offer your support to make X happen or threaten to block her from achieving X.
This is not pretty, but in a democratic society, it leaves everybody more or less equaly frustrated with the compromise; while at the same time nobody's deepest needs and wants get ignored.