In general, seems that follow the CDC guidance make a lot of sense and close this discussion: https://www.cdc.gov/coronavirus/2019-ncov/vaccines/fully-vaccinated.html
Fully vaccinated people can resume activities without wearing a mask or physically distancing, except where required by federal, state, local, tribal, or territorial laws, rules, and regulations, including local business and workplace guidance.
= If the local laws still require mask, you have to wear it.
COVID-19 vaccines are effective at protecting you from getting sick.
= to reduce the spreading of the virus, is better keep the mask. The vaccine helps, but don't stop the spreading of the virus. In fact:
Even after vaccination, you may need to continue taking all precautions.
If you’ve been fully vaccinated:
You still need to show a negative test result or documentation of recovery from COVID-19 before boarding an international flight to the United States.
= even if full vaccinated, you could be infected! Be caution!
And:
You should still get tested 3-5 days after international travel.
For now, if you’ve been fully vaccinated:
If you travel, you should still take steps to protect yourself and others.