Can we be exempted from COVID testing if we’ve been vaccinated?

Not at this point. According to the BC Reopening site (bit.ly/BCReopenFAQ) “Vaccinated students are still subject to asymptomatic surveillance testing, but as of 3/8/2021, per the Massachusetts Department of Public Health, students who have gotten two doses of the Moderna or Pfizer COVID-19 vaccines or one dose of the Janssen (Johnson & Johnson) COVID-19 vaccine more than 14 days ago, are not required to quarantine following an exposure.”