There are many issues surrounding this entire topic. One of which is this:
Were vaccine' passports to be introduced, what would they look like and how would they be used? I have the NHS app (in addition to the Covid app). The security issue is well addressed; photo ID has to be uploaded, identity checked electronically plus you have to take a short video of yourself talking a few numbers. This is all then subject to a final manually performed review before health record access is allowed. So, use this app then?
Well, the app doesn't have a photo of the registered user on display, so if this app is used to show vaccination status. how does the person/organisation that's being shown it know that not relates to the holder (someone else could carry your smartphone)?
What about those that don't have or want a smartphone. Even amongst those that have smartphones, do they all want to go through the rigmarole of registering, etc. There are very many who don't have smartphones; should they be excluded just on the basis of that choice? There are many in my part of the world that are in their 70s and 80s who don't have smartphones. Many do enjoy going down to the social club for a drink though. Is it game over for them on that score then?
OK, so don't use a smartphone app (I have seen talk of using the Covid app, but again no photo is shown on that and no identity checks inbuilt). Paper document then?
So, the NHS sends all that have received both doses of vaccine a certificate. Still no photo on that; the NHS does not have photos as a normal part of your health record. Hence, anyone with a certificate could just lend it to others, along as they looked about the same age and sex of the named holder. Plus the potential for forgery is immense.
Even if a foolproof method is developed, what then? OK, you go to the pub. You show your document to whom? When? (on entry, or drinks order, or..?). It may be a QR type code. Who pays for the scanning equipment. Will the QR code bring up your photo? (doubt it, so see problems above). Suppose you enter in to a pub and don't show your pass and nobody asks? Who's going to 'police' it all? The onus may well be on the publican, but in reality will there really be inspectors (or police) going in to pubs and asking everyone for their vaccine pass? We're now in to very dangerous territory.
Publicans could well say 'no pass, no entry. But that means paying people at the door permanently checking on all who enter. Who pays for that? Plus, suppose entry is gained through use of a fraudulent document; who's responsible for that? Who would even know? (unless we have those roving inspectors).
It's far too early to pass judgement on this until the actual mechanics, in some detail, are published.