Vaccinate All Children Act of 2019 This bill prohibits the Department of Health and Human Services from awarding grants to public entities of a state for preventive health service programs unless the state institutes certain vaccination requirements for its public schools. Specifically, a state must require each student in public elementary or secondary school to be vaccinated in accordance with the recommendations of the Advisory Committee on Immunization Practices. The bill provides an exception for students whose health would be endangered by vaccination in the opinion of a physician conforming to the accepted standard of medical care.