Youre right. Its very difficult to build bridges during a war. As an individual, obviously you can reach out to the people you know. As a group, I dont have any good ideas.
There is something that my husband and I both do (which I neglected to mention), and I've suggested it to others, and that is to keep the pro-life t-shirts ON in day-to-day living that one wears at Life marches. The ones we wear say CHOOSE LIFE on them and they are on bright green t-shirts (picture shown). We end up wearing these to water polo matches, when we go out for walks or jogs, even to Whole Foods (my husband received a 30-second or so glare from one older shopper who I'm assuming didn't agree with the message). We don't really "plan" the wearing of these shirts usually; they just come up next in the closet, and we don't pass them by.
I contribute to the Just One Life movement. Its not much, but its something.
I read about Just One Life. I see they are from Israel and assist Israeli families. Are you from Israel? There are organizations like that in America, too. I had a link on one (that I misplaced) that is run by nuns in New York I believe. Anyway, the more of these organizations, the better ... as you well know. :)