It's really not an either-or situation. You can encourage people to be generally healthier, and also encourage them to get vaccinated (or force them).
And if you compare the two, the vaccine is much closer to a magic cure - it's very dependable and takes "1 month" to work (assuming a two shot vaccine). Whereas encouraging people to be less obese is both incredibly hard (as decades of campaigns prove), and even in the best case scenario, would take a long time for most people.
People should definitely be encouraged to get vaccinated too, I agree. But there should be no institutionalized discrimination against the unvaccinated, just as we shouldn't discriminate against the obese to encourage them to eat less.
And if you compare the two, the vaccine is much closer to a magic cure - it's very dependable and takes "1 month" to work (assuming a two shot vaccine). Whereas encouraging people to be less obese is both incredibly hard (as decades of campaigns prove), and even in the best case scenario, would take a long time for most people.