Israeli Prime Minister Benjamin Netanyahu could soon be ousted from power by a controversy over the most entrenched and right-wing faction in his coalition-government—ultra-Orthodox Jews. The ultra-Orthodox, also known as the Haredim, have been exempt from military service, as well as many other social and political obligations, since the founding of Israel as a state in 1948. Last month, a high court ruled that the military exemption must end. The ruling will be appealed, but meanwhile the Haredim’s yeshivas—the hundreds of schools where young men study the Torah (and little or nothing else)—will lose their government funding. Now Netanyahu must...