I am not sure what you want to get at but if someone wants to be treated like being vaccinated, they should have to proof that they actually are. Anything else incentivizes behaviour that undermines the efforts to get a grip on the pandemic (i.e. it would let the unvaccinated flaunt the rules by just claiming that they no longer pose a threat to others and the pandemic would happily rage on).

We do not implement these measures here (Germany) at the moment. Anyone can visit stores or e.g. retirement homes without having to show a negative test result or proof of vaccination. Before easing the measures, people with proof of vaccination were treated like having a negative result in general, i.e. they could do all the things that others also could but without the hassle of having to be tested.