SITTWE, Myanmar — The Myanmar government has given the estimated one million Rohingya people in this coastal region of the country a dispiriting choice: Prove your family has lived here for more than 60 years and qualify for second-class citizenship, or be placed in camps and face deportation. The policy, accompanied by a wave of decrees and legislation, has made life for the Rohingya, a long-persecuted Muslim minority, ever more desperate, spurring the biggest flow of Rohingya refugees since a major exodus two years ago. The crisis has become an embarrassment to the White House ahead of a scheduled visit...