Solve cultural conflicts by intermarriage.
Babies are born innocent.
The hatred of the other culture runs deep, is historically justified, and indoctrination begins at birth. No rational argument (e.g., promoting "tolerance") can reverse it later in adulthood.
But love (and perhaps only love -- the second strongest instinct) can conquer all because of the biological imperative to procreate. For a couple in love, between the two of them, the quibbles of the real world seem just not that important anymore. With love, they will find a way to work out their cultural differences.
How can we implement this? We need a mechanism by which young people of opposing cultures can meet, ideally during their rebellious teenager phase when they are most likely to be able to reject the hatred with which they've been indoctrinated since birth. Perhaps the education system.
After falling in love, the couple, and especially their children, must be given a legally protected class, and discrimination against them is prohibited and severely punished. Crimes against them are prosecuted as hate crimes and punished extra severely. Speech against them is punished as hate speech. (When is it justifiable to limit freedom of speech? How about for trying to solve a centuries old conflict for which so much blood has already shed?) These protections especially include the couple's protection from their parents and relatives, who will likely be upset at their relationship. Extend laws for emancipated minors, as well as welfare for them as they may now be unsupported by their families. The state recognizes that THEY ARE THE FUTURE FOR PEACE.
The solution thus described, we can see why a cultural conflict persists for generations, how the hate manifests itself on very personal levels. Parents go to great length, for example segregated private schooling or a segregated neighborhood (or country!), to prevent their children from meeting the enemy. The commandment that one must marry within the culture is the most important commandment, and the threats of shunning, excommunication, disinheritance for violating it keep the children in line just in case the childhood indoctrination wasn't enough. All this is couched in a language of "preserving the culture". No, culture is not something to be mindlessly preserved; it is something to be built by each new generation, to improve upon the failures of ancestors.
It will be a bold move for a culture to abandon the current adult generation as already "lost", the hate too deeply entrenched, and to take the leap of faith and place its hope in the rebellious teens of the next generation. I cannot imagine a democracy making such a move (but I would be glad to be proved wrong): the parents will outvote the children, if not by voting age then by sheer numbers. The only way I can see this happening is in a absolute monarchy or dictatorship where an enlightened leader can unilaterally implement this and inflict punishment on any who may oppose with him/her. Perhaps an emirate?
Inspired, among other things, by Hinduism: why does Hinduism have so many gods? Because two cultures met, mixed, and formed a new culture with the set union of their gods, and this happened thousands of times. This can work!
