- Unvaccinated people transmit the virus at a higher rate.
- Transmission leads to more illness.
- More illness leads to overcrowded hospitals and worse outcomes for everyone needing care.
Therefore a “personal choice” can lead to public concerns, making this a public health issue, and actually same could be said for your argument about overeating. Heart disease is a major public health concern, which is why some jurisdictions banned sugary drinks in children’s school lunches.
When using n-order impacts to determine when personal choices become public concerns, it's just a matter of determining where one draws the line. This will undoubtedly lead to differences in opinion on where that line should lie.
For example, even two people who are in support of universal mandatory vaccination many differ on the level of force the government should use gain compliance.
Anecdata warning: Over half of my wife’s healthcare colleagues refuse to get vaccinated. These are people who regularly treat the extremely frail and immunocompromised.
https://www.science.org/content/article/having-sars-cov-2-on...
https://www.medrxiv.org/content/10.1101/2021.08.24.21262415v...
And there's more to immunity than antibodies.
https://www.fda.gov/news-events/press-announcements/coronavi...