The basic method of determining whether an infringement of rights is a justified limitation is to ask the following:
- Does the limitation serve an important public purpose?
- Is it rationally connected to that purpose?
- Is it proportional to that purpose? (Does it impair the right by no more than is reasonably necessary, and do the benefits outweigh the limitation of the right?)
And if you stop to think about it, the answers to those questions are yes, yes, and (almost certainly) yes. Preventing the spread of Covid-19 is an important public purpose. Vaccination prevents spread, and focusing those at highest risk is clearly a good way of doing that. Proportionality depends on the disease: what's proportional for a disease like smallpox which kills people is obviously overkill for a disease like the common cold which merely poses a mild inconvenience. But this is clearly on the killing people end of the scale, which justifies greater intervention. As for where the balance lies, the High Court looked at exactly this question in GF v Minister of COVID-19 Response [2021] NZHC 2526 (the anti-vax customs worker case) and concluded they were proportional. While the vaccine mandate is wider than that on border workers, I don't see any reason to think that basic analysis would change. While more details could emerge, at this stage it doesn't seem like an obvious infringement of human rights.
Update: Clarified that any discriminatory effect is indirect.