They're not banned from buying groceries, they're banned from entering the stores - which unquestionably would lead to them spreading the virus more than vaccinated people entering stores.
They're still allowed to do pickup and delivery orders. Or better yet, get vaccinated.
edit: in the information I linked it is made clear that vaccinated folks _can_ spread the virus. That is true and I never said otherwise. The fact is they spread the virus at much lower rates, for shorter periods of time, than unvaccinated folks. For this reason people should wear N95s when interacting with folks outside of their bubble. In my experience vaccinated folks are more likely to wear their masks, and properly, as well, but I've got no data on that.
I thought it's been established that the vaccinated spread the virus just as vaccinated do [1]. The vaccines might help the person taking it, but that isn't even clear anymore since the vaccines were not engineered for this variant.
This article [1] has some good info regarding transmission in the context of the quote in your source.
While mRNA vaccines – produced by Pfizer and Moderna – continue to offer some level of protection against transmission of omicron, other vaccines – such as Johnson & Johnson, Sinopharm and AstraZeneca – offer “almost no defense,"
“It gets very easy to misconstrue,” Dowdy said. “If someone asks, do vaccines prevent infection, and you have to give a yes or no answer, then the answer is no, they’re not a perfect blockade. But do the vaccines offer some protection against infection? The answer is yes.”
