A private school in the fashionable Design District of Miami sent its faculty and staff a letter last week about getting vaccinated against Covid-19. But unlike institutions that have encouraged and even facilitated vaccination for teachers, the school, Centner Academy, did the opposite: One of its co-founders, Leila Centner, informed employees “with a very heavy heart” that if they chose to get a shot, they would have to stay away from students.In an example of how misinformation threatens the nation’s effort to vaccinate enough Americans to get the coronavirus under control, Ms. Centner, who has frequently shared anti-vaccine posts on Facebook, claimed in the letter that “reports have surfaced recently of non-vaccinated people being negatively impacted by interacting with people who have been vaccinated.”“Even among our own population, we have at least three women with menstrual cycles impacted after having spent time with a vaccinated person,” she wrote, repeating a false claim that vaccinated people can somehow pass the vaccine to others and thereby affect their reproductive systems. (They can do neither.)In the letter, Ms. Centner gave employees three options:Inform the school if they had already been vaccinated, so they could be kept physically distanced from students;Let the school know if they get the vaccine before the end of the school year, “as we cannot allow recently vaccinated people to be near our students until more information is known”;Wait until the school year is over to get vaccinated.Teachers who get the vaccine over the summer will not be allowed to return, the letter said, until clinical trials on the vaccine are completed, and then only “if a position is still available at that time” — effectively making teachers’ employment contingent on avoiding the vaccine.Leila Centner at an event in Miami in 2019.Romain Maurice/Getty Images for Haute LivingMs. Centner required the faculty and staff to fill out a “confidential” form revealing whether they had received a vaccine — and if so, which one and how many doses — or planned to get vaccinated. The form requires employees to “acknowledge the School will take legal measures needed to protect the students if it is determined that I have not answered these questions accurately.”Ms. Centner directed questions about the matter to her publicist, who said in a statement that the school’s top priority throughout the pandemic has been to keep students safe. The statement repeated false claims that vaccinated people “may be transmitting something from their bodies” leading to adverse reproductive issues among women.“We are not 100 percent sure the Covid injections are safe and there are too many unknown variables for us to feel comfortable at this current time,” the statement said.The Food and Drug Administration, the Centers for Disease Control and Prevention, the World Health Organization and many other authorities have concluded that the coronavirus vaccines now in emergency use in the United States are safe and effective.The Centner Academy opened in 2019 for students in prekindergarten through eighth grade, promoting itself as a “happiness school” focused on children’s mindfulness and emotional intelligence. The school prominently advertises on its website support for “medical freedom from mandated vaccines.”Ms. Centner founded the school with her husband, David Centner, a technology and electronic highway tolling entrepreneur. Each has donated heavily to the Republican Party and the Trump re-election campaign, while giving much smaller sums to local Democrats. In February, the Centners welcomed a special guest to speak to students: Robert F. Kennedy Jr., the prominent antivaccine activist. (Mr. Kennedy was suspended from Instagram a few days later for promoting Covid-19 vaccine misinformation.) This month, the school hosted a Zoom talk with Dr. Lawrence Palevsky, a New York pediatrician frequently cited by anti-vaccination activists.Kitty Bennett