The rise of Robert F. Kennedy Jr. from fringe figure to the prospective head of U.S. health policy was fueled by skepticism and distrust of the medical establishment—views that went viral in the Covid-19 pandemic. People once dismissed for their disbelief in conventional medicine are now celebrating a new champion in Washington. Scientists, meanwhile, are trying to figure how they could have managed the pandemic without setting off a populist movement they say threatens longstanding public-health measures. Lingering resentment over pandemic restrictions helped Kennedy and his “Make America Healthy Again” campaign draw people from the left and the right, voters...