An interesting argument on the constitutionality of vaccine passports.
“The concept of vaccine passports has opened a new fissure in the COVID culture wars. Many liberals and libertarians—and a slim majority of Americans—support them, while many conservatives call them unjust, even unconstitutional discrimination. On this last point, however, U.S. constitutional law is clear: The government can limit certain rights and privileges to the vaccinated, especially during a pandemic. So the more pertinent question now isn’t whether vaccine passports are allowed; it’s whether they are required—whether the Constitution entitles vaccinated people to receive exemptions from many COVID restrictions. We believe it does.” (Emphasis mine)
Personably, I do not think they are necessary as cards are issued at time of vaccine. However, saying that the Constitution “requires” them to be issued is compelling, to a point.
As far as private businesses requiring them, that is up to the businesses themselves.