In July 2020, in the middle of the raging coronavirus pandemic, she wrote an opinion essay suggesting that schools and child care centers might be able to reopen safely, noting that working parents “can’t wait around forever.” In her popular parenting books, she tossed away longstanding medical guidelines, arguing that an occasional sushi roll and glass of wine are safe during pregnancy and that breastfeeding is overrated. More recently, she has cast doubt on whether students need to wear masks or remain physically distanced at school. This steady stream of counterintuitive advice has made Dr. Oster a lodestar for a certain set of parents, generally college-educated, liberal and affluent. Many had first latched onto her data-driven child-rearing books. Her popularity grew during the pandemic, as she collected case counts of Covid-19 in schools and advanced her own strongly held views on the importance of returning to in-person learning. Some parents said, half-seriously, “Emily Oster is my C.D.C.” But others — teachers, epidemiologists and labor activists — criticized her, pointing out that she was not an infectious disease expert, nor did she have any deep personal or professional experience with public education.