I just can't imagine that being true at all. First off, mask mandates have already been lifting in the states with the most vaccine hesitancy. There is no mask mandate through most of Florida, included.
The places that have had their mask mandates lifted are not achieving higher vaccination rates.
Making masks voluntary instead of mandatory does not suddenly motivate people to get vaccinated.
Most critically -- It is impossible to have different requirements for vaccinated vs un-vaccinated people. The CDC really can only make recommendations and most of their recommendations are always going to be strictly voluntary. Whether you have now feel you can unmask at your backyward BBQ -- totally voluntary.
For those areas that do "mandate" masks -- whether grocery stores, some localities, Disney World -- It's physically impossible to have different requirements for vaccinated vs un-vaccinated people. What's the CDC going to recommend and have WDW follow? Tell people they can't take off their masks if their vaccinated, and have cast members walking around doing random spot checks of people's vaccination cards?
But this should be the incentive to get vaccinated -- When everyone (or almost everyone) gets vaccinated, we can lift all the mitigation measures!
Do you want to be the bozo holding up the lifting of all mitigation measures?!?!?