TOKYO — On Okinawa, long-suffering residents are fed up with U.S. Marine Corps helicopters relentlessly beating above their rooftops. In Tokyo, an assertive new Japanese government is reopening basing questions that the U.S. military thought were settled. Even on Guam, a U.S. territory in the Pacific where support for American military bases was taken for granted, local officials are suddenly asking the Pentagon to slow a huge expansion plan. Sixty-five years after the U.S. victory in World War II cemented America’s military presence across the Far East, rumblings of discontent are growing. Nationalism, not-in-my-backyard syndrome, the rising influence of China...