As soon as Anna Weber Kneitel learned San Francisco Bay Area pharmacies had opened appointments for Covid-19 vaccines for young children, she booked the closest one she could find for her seven-year-old son.

But across the country in Michigan, Rachael LaPlante said she was planning to hold off on getting the shots for her seven-year-old son, despite being fully vaccinated against Covid-19 herself.

After months of anticipation, the US Centers for Disease Control and Prevention on Tuesday gave...