Based on some posts in the schedule thread, I also want to pass on what Dr. Mrs. G (see what I did there) says about transmitting the virus after vaccination.
Recommending that the vaccinated continue to wear masks and take other precautions is done out of an abundance of caution because there is a theoretical risk of a vaccinated person transmitting the virus when fighting off an infection of his/her own. There is no evidence that people who have been vaccinated are a substantial risk to infect others. In fact, it is highly probable that any such risk is very small if not insignificant.
I personally also think the advice comes also because officials want to maintain a social norm of masks and distancing for a while longer at least. If individuals stop wearing masks once vaccinated, then it sends a subtle signal to everyone else to do the same. Way too early for that.
FWIW, Dr. Mrs. G has been seeing patients throughout the pandemic (70+ per week), always in a mask. She will continue to do so for the time being.