I don't think will happen, in terms of denying care on the basis of self-inflicted injury, as this means the sick person returning to spread the virus in the community, and isn't consistent with how 1st world countries deal with the complications of obesity and smoking.
On the other hand, I, too, have wondered at what point we presume those who want to be vaccinated can be, get on with our lives and let those who indulge paranoia lie in the bed they made? That is the question.
In fairness, this mindset only applies to 1st world countries with widespread availability, and let's be mindful a small subset may have contraindications, or be on immunosuppressive therapy so that vaccination doesn't work well. I am aware the counter argument is that just because a few people have to 'live in a bubble' doesn't mean the rest of us will.
A rising tide lifts all boats, and a falling tide lowers them. Even someone with a career that doesn't directly rely on tourism (off-shore banking, perhaps?) may eat at restaurants and use other services, or have friends and relatives, where tourism matters. I'll be curious to see if any posters who live and work in the Caymans say this is an issue.