They will not be logically consistent, and thankfully. Because if they were, we'd be going towards a really fucked up world.

Generally you're right though. On their logic if pushed to its conclusion, all the totalitarianism in the world could be justified if it saves one person from dying of the flu or from dying of obesity.

Are you saying it's as easy to lose weight as it is getting vaccinated? Obesity is a disease.

It's easier. For the majority of people, all you need to do is eat less. If you argument is that obese people do not have the ability to eat less, that is a much different discussion (with some implications I don't think many are comfortable with).