That advice is based on "we don't know if you can spread it". Evidence is starting to show it may indeed reduce/stop transmission.

https://www.nbcchicago.com/news/local/dr-fauci-explains-why-...

> "It may be that we will show that if the level of virus in your nasopharynx because you're vaccinated is so low that you don't have to worry about transmitting, that's going to be a game changer for what a vaccinated person can or cannot do," Fauci said.

> The doctor explained that if the findings are corroborated, Americans will likely see a pulling back on some restrictions, but emphasized "we're not there yet."