The path to beating the coronavirus was clear, but Kelley Vollmar had never felt so helpless.

As the top health official in Missouri’s Jefferson County, Ms. Vollmar knew a mandate requiring people to wear masks could help save lives. She pressed the governor’s office to issue a statewide order, and hospital leaders were making a similar push. Even the White House, at a time when President Trump was sometimes mocking people who wore masks, was privately urging the Republican governor to impose a mandate.

Still, Gov. Mike Parson resisted, and in the suburbs of St. Louis, Ms. Vollmar found herself under attack. A member of the county health board called her a liar. The sheriff announced that he would not enforce a local mandate. After anti-mask activists posted her address online, Ms. Vollmar installed a security system at her home.

“This past year, everything that we’ve done has been questioned,” said Ms. Vollmar, whose own mother, 77, died from complications of the coronavirus in December. “It feels like the Lorax from the old Dr. Seuss story: I’m here to save the trees, and nobody is listening.”