And I think I agree with you, that the essential difference is how easy it is to get vaccinated.
I probably come to different conclusions because I know people for whom it's not "easy". This is because they are fearful of vaccines, mistrust authority, are uneducated or are paranoid. I think there is a parallel between an alcoholic slowly ruining their life through denial of the effects of drinking, and someone refusing a useful vaccine due to fear. In both cases, stigma may help them change course, but in my experience is is more likely to entrench the behaviour. Thus I don't think it should be used.
At some point people need to stop being so lenient on health suppliers. They are implicitly demanding society trashes itself to avoid them having to hire and train. It's endemic now, there is no cure, the treatment is mostly still oxygen+drugs. There's no excuse.
https://www.wfae.org/health/2021-09-30/novant-says-9-of-10-c...
Your points were addressed implicitly, but I can do so explicitly at your behest:
Obesity and alcoholism aren't preventing people with other conditions from seeking medical care because the current medical system (at least in western nations) can account for and manage these conditions successfully, unlike COVID which has consistently resulted in resource, capacity, and utility shortages throughout the pandemic thereby posing an undue risk to general welfare and the lives of others.
I also say this as someone who's been both obese and not obese: unlike a decision to refuse a life-saving vaccine, refusing to eat is far, far harder. And as someone who refuses to drink specifically because I know my own tendencies towards addiction, I empathize with those who started drinking socially and suddenly found themselves trapped by the vice grip of an alcohol abuse disorder.
None of these compare to to choosing to refuse a vaccine without sound medical grounds.
There's nothing much to debate here; the topics you flagged are pretty personal topics for me, so I'll gladly and passionately defend against their misuse in debate.