Which, I don't think, would be the actual implementation that businesses enact because of the blowback.
However, businesses MIGHT go the route of 'okay, if you're not vaccinated, you need to over in this area for seating (restaurants, sports venues, etc), wear a mask at all times, wear a mask if you're doing this activity, follow distancing requirements, or any combination of spread mitigation to protect our other patrons'.
So businesses wouldn't have COMPULSORY vaccination, but the vaccine passport would allow them to implement health guidelines based off immunization status.