If the Palestinian Entity is considered a full fledged legal state, and at this stage they are not. Any attempt to give them territory would fall under the rules of Cession (explained well in Shaw, 1997, Pp 339 & following). This would require the Palestinians to respect third party rights to the land (such as Jewish rights to the visit the graves of their ancestors without danger). The fact that the Palestinians have yet to show that they would respect International legal rights of the Jews in their midst if Israel were to fully withdraw from the West Bank, makes it foolish and immoral to consider such a withdrawal, and illegal to implement such a withdrawal.
If the Palestinian Entity is a nonstate organization, and at this stage, they are. Any attempt to give them land would fall under the rules of Succession. (Shaw, 1997, Pg 930) And that would mean that Israel would need to fully consider the rights of the owners of the religious sites in question. As the State of Israel never annexed sites such as the Cave of the Patriarchs in Hebron, and they preserved the rights of Jews to practice ritual and dwell near the Holy Sites of the West Bank, they have defacto declared the Jews of the West Bank as the rightful owners/representatives of these Holy Sites. Therefore any attempt to surrender West Bank Holy Sites, would require some sort of binding referendum of the Israelis in the West Bank as to the future of the Holy Sites.
This is not the case with East Jerusalem, which in its entirety, including all its Holy Sites has been annexed already by Israel. If however, Israel's government would reject its ownership of the East Jerusalem Holy Sites, it would require two referendums. One of Jews within the Green Line, and only if the Jews forsake their religious rights would it make sense to bother with a full referendum of all Israelis, Jew and Gentile alike, to seek political permit of any transfer. If, however, indeed the very freedom of religion for the Jewish People realistically depends on their possession of all their Holy Sites, then they cannot choose to surrender that which they must have. Primal law trumps political expediency every time.