SAN FRANCISCO Growing up in eastern China, Panshu Zhao fell in love with America. He read the Bible his parents gave him, watched Hollywood movies and studied the ideals of democracy. He jumped at the chance to attend graduate school at Texas A&M University. In 2016, Zhao enlisted in the U.S. Army as part of a special recruitment program offering immigrants in the country legally a path to citizenship. The future, he said, was bright. Now, he is one of the dozens of immigrant recruits and reservists struggling with abrupt, often unexplained military discharges and canceled contracts. They traded being...