Vilified, threatened with violence and in some cases suffering from burnout, dozens of state and local public health leaders around the U.S. have resigned or have been fired amid the coronavirus outbreak, a testament to how politically combustible masks, lockdowns and infection data have become. One of the latest departures came Sunday, when California’s public health director, Dr. Sonia Angell, was ousted following a technical glitch that caused a delay in reporting hundreds of thousands of virus test results — information used to make decisions about reopening businesses and schools. Last week, New York City’s health commissioner was replaced after...