When a coronavirus vaccine becomes available in the United States, the federal government and states will face a crucial choice: Should all or most residents be required to get the novel coronavirus vaccine?

Or should it be required only for school children, with a medical exception allowed, and for groups like front-line health-care workers? Some officials might want few or no requirements at all because they think enough people are likely to get the vaccine voluntarily or have immunity from an infection to halt the spread of the disease.

But in states like Oklahoma, efforts to require an...