More school districts are loosening mask and quarantine requirements as Covid-19 vaccines roll out for younger children and cases have dropped from the summer’s Delta surge.

Florida’s Miami-Dade County Public Schools system said Tuesday it would allow all parents to opt out of having their children, including elementary-school students, wear masks in school. That widened a decision last week that applied to parents of high-schoolers and middle schoolers.

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More school districts are loosening mask and quarantine requirements as Covid-19 vaccines roll out for younger children and cases have dropped from the summer’s Delta surge.

Florida’s Miami-Dade County Public Schools system said Tuesday it would allow all parents to opt out of having their children, including elementary-school students, wear masks in school. That widened a decision last week that applied to parents of high-schoolers and middle schoolers.

A Charleston, S.C., school-district mandate requiring students, staff and visitors to wear masks indoors expired Wednesday after the school board decided not to extend it. And Ohio last month said students exposed to Covid-19 can now stay in school rather than quarantine if they wear a mask for up to 14 days—or fewer if they don’t have symptoms and test negative after day 5 to 7.

At the beginning of November, 17 states required masks in their schools; 26 didn’t and seven states prohibited mask requirements, according to the Kaiser Family Foundation. At the start of the school year in August, as the highly contagious Delta variant of Covid-19 was spreading quickly and infecting children, nearly half of parents polled by Gallup said that all school students should wear masks at school.

The availability of a vaccine for children has shifted the conversation. On Nov. 2, the Centers for Disease Control and Prevention backed the use of the Pfizer Inc.-BioNTech SE Covid-19 vaccine in children ages 5 to 11 years. Efforts to relax school restrictions so quickly after the vaccine’s launch reflect how eager many officials and parents are to get back to normal—and will serve as a key test in the country’s ability to manage the virus.

White House Covid-19 coordinator Jeff Zients said Wednesday that the administration estimated that 900,000 children ages 5 through 11 would receive a first dose of the coronavirus vaccine by the end of that day. He added that 700,000 additional appointments had been made at local pharmacies.

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“After several months, we’ve seen that in-person schooling can be functional,” Emily Oster, an economics professor at Brown University and author of books and articles on families and parenting. “Now how do we take the last steps toward normalcy?”

In the Northeast, state and city officials have recently been talking more about the prospect of easing of Covid-19 safety protocols in schools. New Jersey Gov. Phil Murphy said this week that he could see a phased-in lifting of the state’s mask mandate, due to expire Jan. 11.

New York City Mayor-elect Eric Adams has said he hopes students will be able to stop wearing masks by year-end. Pennsylvania Gov. Tom Wolf

this week said he intends to return decisions about masks in schools to local leaders when a statewide mandate expires in mid-January.

Changes in Covid school policies are contentious. Quarantine disruptions have been hard on working parents, and some say masks make it harder for kids to understand emotional and social cues. Other parents worry that lifting mandates risks their children’s health.

Children aged 5 to 11 started getting their first doses of Covid-19 vaccines Wednesday after the CDC recommended use of the Pfizer-BioNTech shot for that age group. Some parents said they were eager for kids to get vaccinated and return to normal life. Photo: Maddie McGarvey/WSJ The Wall Street Journal Interactive Edition

“I still feel strongly that schools should maintain Covid-19 safety protocols until the rate of community transmission decreases,” says Ren Tonsa, a mother in Delaware County, Pa., whose 11-year-old daughter has Down syndrome and is susceptible to serious respiratory problems. Ms. Tonsa says she hopes her daughter, out of school since March 2020, will go back in January.

The CDC still recommends universal indoor masking at school and, when possible, a physical distance between children of at least 3 feet. Some scientists and public-health analysts worry that states and districts may loosen school protocols too soon. Covid cases are on the rise again in places including California, and the summer’s Delta surge illustrated how quickly the pandemic can change course.

The methods by which school districts are easing Covid-19 protocols vary widely, often influenced by the local political climate, says

Matt Ferron, superintendent of Hanover Public Schools in Hanover, Mass. His state lets a school apply to lift the mandate for vaccinated people once 80% of students and staff are vaccinated. A neighboring school district has reached that goal, he says. But his hasn’t.

People are “intensely divided and angry” over the mask mandate.

In August Massachusetts unveiled a revamped quarantine protocol with a “test and stay” policy that is catching on with some other school districts too. Last year, anybody directly exposed to Covid-19 had to go home to quarantine. This year, a student who is exposed can stay in school, though if unvaccinated must take a rapid test every day through what would normally be the quarantine period.

Mr. Ferron says his schools have also started to loosen restrictions on school visitors, allowing parents to come in to act as room helpers and read to the kids.

“We’re not saying no to everything anymore,” he says.

—Sabrina Siddiqui and Ben Chapman contributed to this article.

Write to Betsy Morris at betsy.morris@wsj.com