This whole issue is laughable, and actually reveals more about the way Israelis think than anything else.
The UNESCO resolution only:
1. Named it as an endangered heritage site.
2. Decided under which nation it should be regarded.
Israelis seem outraged by number 2.
They seem to be implying that considering it Palestinian means that Jews have no connection to it. This is quite the bizarre interpretation. This projection reveals so much about how Israelis conflate nationality with ethnicity and religion. A site can easily be Jewish and Palestinian. There is nothing contradictory there, Palestinian is an inclusive identity that literally anybody could be a part of, you don’t have to be a special religion or ethnicity.
Second of all, under any peace deal or arrangement, Israelis should be able to visit with no problem. Same as Palestinians should be able to visit their holy places inside “Israel proper” as well.
Third of all, Al-Khalil is a Palestinian city. It is inhabited almost exclusively by Palestinians. Those not, are a relatively minuscule amount of illegal settlers. Not even in the most broad interpretation of international law can anyone claim that it is a part of Israel. Is Israel the custodian of every Jewish site in the world? Does it get to exert control/sovereignty over Jewish sites in other countries?
Is this what Israel wants? Control over it? Then, if this is the case, will it hand over control of Muslim and Christian sites inside Israel to the Palestinians? If no, why not?
When you ask about it this way, it becomes clear how obtuse and greedy Zionist objections are. It is not merely about the sites, it is about acknowledging Palestinians and their existence.
Again, the UNESCO resolution said literally nothing about its importance to anyone. This rhetoric was simply created to draw attention away from the expansionism and entitlement Israelis feel towards everything between the river and the sea.
How dare those Palestinians exist, and a site in Palestinian territory, inhabited by Palestinians, is in fact, considered Palestinian.