JERUSALEM — It was a typical day at the shrine around what many believe is the tomb of Jesus in Jerusalem’s Old City. A Greek Orthodox choir sang inside a room facing the baroque structure. But the voices were drowned out when chanting Armenian priests and monks circling the shrine raised theirs.

“Sometimes they punch each other,” Farah Atallah, a church guard wearing a fez, observed with a shrug.

Mr. Atallah is a seasoned witness to the rivalries among the Greek Orthodox, Armenian Orthodox and Roman Catholic communities that jealously share — and sometimes spar over — what they consider Christianity’s holiest site, inside the Church of the Holy Sepulcher. MORE