We know those vaccinated are greatly protected. However the CDC states there is much we do not know about their impact on others. As recently as February 9, 2021, the CDC updated their guidance for those vaccinated:
Although COVID-19 vaccines are effective at keeping you from getting sick, scientists are still learning how well vaccines prevent you from spreading the virus that causes COVID-19 to others, even if you do not get sick.
If you are vaccinated against COVID-19, you may still be exposed to the virus that causes COVID-19. After exposure, people can be infected with or “carry” the virus that causes COVID-19 but not feel sick or have any symptoms. Experts call this “asymptomatic infection.”
For this reason, even after vaccination, we need to continue using all the tools available to help stop this pandemic as we learn more about how COVID-19 vaccines work in real-world conditions.