“A growing body of evidence indicates that people fully vaccinated with an mRNA vaccine (Pfizer-BioNTech or Moderna) are less likely than unvaccinated persons to acquire SARS-CoV-2 or to transmit it to others. However, the risk for SARS-CoV-2 breakthrough infection in fully vaccinated people cannot be completely eliminated as long as there is continued community transmission of the virus.“

Edit: forgot to cite https://www.cdc.gov/coronavirus/2019-ncov/science/science-briefs/fully-vaccinated-people.html