For many skeptics, resistance tends to be based not on formal teachings from an established faith leader, but an ad hoc blend of online conspiracies and misinformation, conservative media and conversations with like-minded friends and family members.

“People who have already made up their minds are now looking for ways to continue to exempt themselves from the Covid vaccine,” said Joshua Williams, a pediatrician and assistant professor of pediatrics at the University of Colorado.

Mr. Williams’s prepandemic research into school immunization requirements suggests that most objections described as religious to vaccines are really a matter of personal — and secular — beliefs. After the state of Vermont removed its vaccine exemption for nonreligious personal beliefs in 2016, the proportion of kindergarten students with a religious exemption shot up from 0.5 percent to 3.7 percent, suggesting that most parents who took advantage of religious exemptions did so only when others were not available.