Like many Black and rural Americans, Denese Rankin, a 55-year-old retired bookkeeper and receptionist in Castleberry, Ala., did not want the Covid-19 vaccine.

Ms. Rankin worried about side effects — she had seen stories on social media about people developing Bell’s palsy, for example, after they were vaccinated. She thought the vaccines had come about too quickly to be safe. And she worried that the vaccinations might turn out to be another example in the government’s long history of medical experimentation on Black people.