Changes to official recommendations on Covid-19 vaccines raised concerns that insurers would no longer be required to cover the full cost of the immunization. Hannah Beier/Reuters

Most Americans with health insurance should not have to pay out of pocket for Covid-19 vaccines, even after the US Centers for Disease Control and Prevention added an extra hurdle to getting the shot. But some people could face new costs.

The CDC adopted its vaccine advisers’ vote to shift away from a broad recommendation for Covid-19 immunization; people who want one must now consult with a health care provider, a process known as shared clinical decision-making. However, a prescription is not necessarily needed.

But the change raised concerns that insurers would no longer be required to cover the full co

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