See my explanation here.
I had not read the dissent when I explained the quote attributed to Thomas - and I know the general law from Smith. I have now read the dissent. I haven't read the underlying case Thomas cited - but it is an exception to Smith which (at least on its face) passes the laugh test.
So you don't have to go chase my other post: Essentially the argument is that state potentially lost the "generally applicable" safe harbor when it allowed people with secular objections (medical exemptions) to continue working as long as they took certain precautions to protect others. That different treatment for secular reasons may have rendered the generally applicable law no longer generally applicable. If so, it's harder to force people to violate their religious beliefs which run contrary to state law (or the equivalent).
I understand the reasoning for NY limiting the exemption to medical exemptions - if it was opened up to all objections, for any reason, it would gut the law. It is a compelling interest (keeping the number of unvaccinated healthcare workers to an absolute minimum), to which the requirement is directly related (only a very few will have true medical contraindications - so a universal rule with a single category of exemptions serves that goal). The question is whether there is another way to serve that interest without treating religious exemptions different from all others.
The truism in law is that the plaintiff wins if the test is strict scrutiny; the state wins if it is rational basis. It isn't always true - but it is most of the time.
So - who knows. But - at least for now - 6 justices aren't interested in resolving that particular question.