HONG KONG — When Hong Kong’s leader invoked emergency powers to ban face masks during protests, she went to great lengths to explain that the city wasn’t in a state of emergency. Rather, she declared, after months of unrest, the city was in a “very critical state of public danger.” The message, and the ban itself, were highly calculated. They were designed to show that the government was taking action to protect public safety while trying not to provoke more violence from protesters. The pro-Beijing camp of government leaders and lawmakers, from moderates like Chief Executive Carrie Lam to the hard-liners, was also determined to deal with the unrest, and not give the Chinese leadership any reason to intervene. “We want to resolve it ourselves,” said Regina Ip, a hard-line member of Mrs. Lam’s cabinet who leads a political party that is popular with police officers. Trying to restore public order without spurring more protests will be hard to achieve, however, and the city’s leadership is already considering imposing other measures to crack down. Starkly different views on just the face-mask ban underscore how irreconcilable the differences between the government and the protesters have become. To Hong Kong’s top leaders,…