The scene was completely surreal: A crying cantor beseeching the Lord in Yiddish-accented Hebrew to hear his prayers; high-octane loudspeakers amplifying the cry throughout lower Manhattan; tens of thousands of black-coated ultra-Orthodox Jews earnestly repeating the Psalms in the freezing cold; some of New York’s finest, duly exasperated; and the looks of astonishment on the faces of unsuspecting tourists who...