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The recent CDC recommendations are guidelines for proper behavior for the fully vaccinated—it is expected that as more of the population are vaccinated that these recommendations will change and allow more interaction. The scenario illustrated by the questioner is contingent upon whether the private setting interaction involves unvaccinated persons who have risk of severe COVID-19.
If the unvaccinated people are from a single household that does not have individuals at risk of severe COVID-19, they can visit with fully vaccinated people indoors, without anyone wearing masks, with a low risk of SARS-CoV-2 transmission. On the other hand, if any of the unvaccinated people or their household members are at increased risk of severe COVID-19, all attendees should take precautions including wearing a well-fitted mask, staying at least 6 feet away from others, and visiting outdoors or in a well-ventilated space. In between any private setting visit between households, all persons should continue to practice physical distancing, masking, and hand hygiene when out in the general public—in other words, the guidance is only for allowances in private controlled settings of small groups (2 households).
The detailed instructions from the CDC are at this link. https://www.cdc.gov/coronavirus/2019-ncov/vaccines/fully-vaccinated-guidance.html#anchor_1615143349134