I think the closer you get to the individual level, the whole empathize/sympathize/see it from another's pov is much more doable than many attempt to do. But what some don't seem to get is that if, for example I do see and understand your pov, it doesn't mean that I believe it to be right, or just, or moral. It means I can see where you get your belief, I can see why you believe what you do. But perhaps I can also see where that belief/practice/action might lead, and I see it as dangerous, immoral, illegal or whatever.
Am I to then, just not offer up and support what I believe to be right in this given area? Am I not to stand my ground for what I see as important/moral/legal/or protective of something or someone?
When the issues and divisions are things of little importance (cross town rivalry sports teams) we need to teach and enforce tolerance, and putting things into perspective. It is only a game. When it is bigger things, on a bigger (state, national, world) scale, and the stakes are much higher (equality, rights, security, survival), the waters get muddied. We aren't as connected as the closer relationships, there are more than one thing dividing us (the sports teams share a town, families, work places, etc., while there is so much more dividing us on the global level, like religion, language, culture, mores).
We, as humans, will never get everyone to cooperate. There will always be evil, and evil must be fought, and if in no other place, conflict will always exist there. Could we all do more to 'get along'? Yes. Will everyone? No.
And all conflict isn't hate. Many seem to want to frame it that way, but it simply isn't true. Dissension is often good and necessary for change as well as the maintenance/establishment of what is good and just and right.