If people are medically unable to take any vaccine then I expect they would still not be able to work in that field. As a comparison, if you are a surgeon and you have Hep. B or AIDS then tough you can’t be one. It’s in the GMC guidance you are not allowed to let your health put your patients at risk. I’d expect to see that applied more widely.
I'm not sure where you got that information from but it is wholly incorrect. If a surgeon, dentist or anybody else in front line medical care, has either HepB or HIV and it has been disclosed to the Health Trust/Board, and the GMC etc, there is absolutely no bar in place blocking that person to practice.
There are possibly an average percentage of HepB or HIV positive people working in the healthcare profession, as in all other professions. As HepB and HIV is now controlled using a broad range of medications (such as antivirals and retrovirals, combination therapy et al) HIV, especially, is much more difficult to pass on - if controlled correctly and many now become undetectable (Google U=U).
If a person was rejected for a job, in any field, for their HIV or Hep status, then this would open a number of floodgates for discrimination. It hasn't been long since the GMC allowed this, granted.
As for not being able to work in a specific field if you haven't - or can't have the Covid 19 vaccine, then this shouldn't be an issue. There is a large proportion of people who cannot have the vaccine for whatever reason, and blocking them from a job is discrimination again on a huge scale.
I can't have the vaccine due to severe allergies (high risk of anaphylaxis), but would that stop me getting a job in, say, GWR's revenue protection team? Absolutely not. As long as all Government and NHS advice is followed, then why should I be stopped?
And if they want a vaccination passport, why not use the little card they give you when you have your jabs? It has the name of the type of vaccine, batch numbers, dates and your name. Same size as a credit card!