The discussions are already loading up whether this is dangerous, unamerican, ripe for civil rights abuses, etc. I think my concern comes even farther back up the chain. Is there any evidence this will actually accomplish anything in terms of public health? It sounds like it might if you imagine infected people boarding airplanes and sneezing their way to New Orleans, but lots of things sound like they might work. Our imaginations are unreliable guides for legislation. In this it is similar to Second Amendment rights questions (there may be distinctions that have not yet occurred to me). There isn't any evidence that proposed gun control legislation will increase safety, and it might actually make things worse. Therefore, the question should not even make it to the table.
I do understand that many reverse this framing and say "First, let us note that this is an infringement on liberties and should be rejected on that basis." I don't object. I may think more like an engineer than a lawyer.
I think the twin solutions are admired for similar reasons. They both make some people feel safer when they imagine simplistic narratives, that is, stories they quickly imagine about how illness could be spread or someone could be shot.
It gets difficult for private companies. An airline might have good data showing that requiring a vaccine ID provides no added safety benefit, but if the public believes it does, they will fly other airlines. Where do you draw the line between not being bullied and just saying "Eh, it's all about advertising and perception anyway. Put on the show and stay in business."
Updates: Someone at National Review does not think there is evidence that a vaccine passport would create any positive benefit. He quotes some interesting people, and notes that some groups have difficulty obtaining a vaccine and others have legitimate reasons for caution.
In the online arguments, I notice that the sides quickly split into people who are opposed to the vaccine itself (and often all vaccines) and thus feel they are being forced to get something unsafe in order to exercise rights of movement and interaction that are foundational as American, versus people who are asserting that all who oppose the vaccine passport are unscientific conspiracy theorists who oppose all vaccines. When those poles are set up, they become self-fulfilling, as the antivaxxers look like the whole other side to the passport-demanders, and inflexible tyrannical sheeple look like the whole of the other side. People who have any view between those poles have a hard time getting heard over the shouting.