Tree of Knowledge
There is a unique and radical understanding on the topic of human deliberation that comes from the esoteric traditions, notably, the Kabbalah where they have anticipated its arrival for some time. It's a technical issue within consciousness that appears when man has reached the limits of reason within the collective consciousness. As Aristotlian logic prohibits the values of true and false occupying the same space, an unconscious, energetic polarization emerges to protect the holding parties, for the same reason that black must be held separate from white lest a muddy, incomprehensible mess ensue, and note here, that, critically, neither is superior though there will be parties that hold each as "their truth".
Observe that the limits of reason were insinuated at the beginning of last century and came to a culmination within philosophy (post-modernism) and physics (superposition and the amorphous clouds of probability). (Religion, of course, has known of it for an indeterminable time.) In any case, and significant to question of developing a tools for conflict resolution is: THERE IS NO RATIONAL SOLUTION. Like Einstein said, a problem can not be solved at the same level at which it was created. In this case the problem is reason itself and treating it like the master, rather than the servant. When such occurs each side will, predictably, see the other as "wrong" or even "evil"--that is just a necessary consequence of the real need to maintain separation within the semi-shared machine called reason or the collective consciousness.
Whether it's mind vs. body, Christian vs. Muslim, the only "synthesis" that one can take in this case, and one that I believe society eventually must take, is one which is a-rational: namely, simply believing in each other for no reason at all. The Hebrews would call it, I think, the completion of the "Tree of Life" which ends the dualism between "good" and "evil". It's interesting that they predicted it's coming and knew of it at all (i.e. that there is a logical endpoint to knowledge and that until such endpoint is reached ,dualisms reigns). It ends 5 millenia of humanity's evolution; that is, 5000 years of struggle of both will and logic only to find that the whole story (as Bertrand Russell learned) is "unsolvable" (which in this context means rationally) -- at such point, the issue becomes one of aesthetics, love, and faith.
Being irrational, the best solution regarding conflict may simply be just to dance, or perhaps follow the bonobos...