Youth Access to Sexual Health Services Act of 2019 This bill authorizes the Department of Health and Human Services to award grants to support the access of marginalized youth to sexual health services such as sexual health education and contraception. Marginalized youth are disadvantaged individuals under the age of 26. Grants may be awarded to state or local health or education agencies, public schools, nonprofit organizations, hospitals, Indian tribes, and tribal organizations. Grants may be used to (1) provide sexual health information to marginalized youth, (2) promote effective communication regarding sexual health among marginalized youth, (3) promote and support opportunities for school-age parents, and (3) train individuals who work with marginalized youth to promote sexual health and the development of safe and supportive environments. Grants may not be used to provide access to health services that (1) are medically unsound; (2) withhold sexual health-promoting or lifesaving information; (3) promote gender stereotypes; or (4) are insensitive or unresponsive to the needs of young people, including youth with varying gender identities and sexual orientations, sexually active youth, pregnant or parenting youth, and survivors of sexual abuse or assault. Unobligated funds for abstinence education are transferred and made available for these grants.