Beckwith's almost certainly referring to the periodic (and still occasionally continuing) riots in the Church of the Holy Sepulcher, built over the (traditional) site of Jesus' crucifixion, burial, and resurrection. There's been conflict over this church ever since the First Crusade turned out the Eastern Orthodox Patriarch of Jerusalem and Brotherhood of the Holy Sepulcher and replaced them with their own Patriarch and custodians.

When the Muslims retook the city, they eventually allowed both groups to use the church. Regular riots resulted over scheduling of services or perceived interference in each others' services; eventually, as Beckwith says, the Muslims were forced to impose a compromise that is still in force. The keys to the church are held by a Muslim family, and nothing can be changed or rearranged in the common areas without consent of all groups. That last clause has led to the perhaps-comic establishment of the "Immovable Ladder": a ladder which a workman had set up in a common area when the last agreement was signed, freezing everything - including that ladder - in place until today.