Can people have completely opposite views? Can a so-called Palestinian believe the exact opposite of what a Jew wholeheartedly believes, when both are certain of their truths?
Torah, the only source of ultimate truth, confirms this contradictory possibility.
Consider an example from Torah's word "abomination", which means absolutely disgusting or hated.
Torah first mentions the word "abomination" in the story of Joseph, when he sets two tables apart for his 2 groups of house guests, for a meal. One table he sets up for his Jewish brothers. For his fellow Egyptians he sets up a separate table. Why this separation? Torah (Miketz 43:32) explains that Egyptians would not share in the beef eaten by the Jewish guests because they regarded sheep as divine. Partaking in such a meal they would deem an abomination. It would nauseate them seeing Jews eating what they considered sacred and divine.
Here then is an example where the same animal is regarded from entirely opposing viewpoints. One view regards the animal as holy, while the other relishes it as edible.
The second appearance of that word in Torah (Achrei Mot 18:22) is when Torah commands the Jews to avoid male homosexuality. The verse says, "And a male you should not bed as you would a woman for that is an abomination."
Is the word "abomination" used in Torah merely as a figurative hyperbole? Is its mention used just to appear stringent but not strictly punishable? Perhaps it just means bad, but not extremely bad?
The 3rd mention of this same word in Torah (Kedoshim, 20:13) answers this question in no uncertain terms: "The man who beds another male as he would a woman, both committed an abomination, both should die, the blood is on their hands."
So we see, what is an abomination to one person can be what another actually aspires for. Two people or two nations can have entirely opposite and contradictory viewpoints.
Of course the final truth between opposing views can only be as Torah deems it. It's up to individuals themselves to learn the real truth because only one side is ultimately correct.