In downtown Chicago, people crawled through the partially shattered exterior window of a Nike store and ran out carrying brightly colored athletic gear and sneakers. On Melrose Avenue in Los Angeles, they ignited garbage cans and broke locks on luxury stores, sweeping up armfuls of designer handbags and jeans. And as night fell on Minneapolis, the heart of widening protests set off by the death of an African-American man in police custody there, business owners stood outside their doors and pleaded with agitators to spare the enterprises that many said they had spent their life savings to build. “I was...