There are so many comments saying "what about people who drink, do sports, drive, eat unhealthy etc."
They just do not compare.
Putting yourself at some level of risk is something that is required in life. Needing to drive to get places, having to walk alone at night as that's the only route from A to B. Any accident someone is involved in you could hypothetically say 'were you not responsible for putting yourself in that situation?'. Should you not have inspected then floor for trip hazards before walking? Should you have not eaten slower to avoid choking on that food?
Issues around obesity, smoking, alcohol, drugs etc are the same. The issues around these are deeply complex and are related to education, mental health, socio economics. There are many variables involved that are not simple to tackle with no straightforward solution. I'm sure if there was a vaccine to tackle emotional binge eating or alcohol dependency people would take it.
And what would be an acceptable level of personal risk, is being a little bit overweight ok? What if you used to do drugs but are clean now? ...finding a criteria would be impossible.
In all those scenarios there are so many variables and complex issues surrounding it and impossibilities to draw a line about what is an acceptable level of personal risk and what isnt.
Where as having a vaccine is simply a choice to have it or to not have it.
FYI I dont agree the UK should deny non vaccinated free treatment as it goes against the principles of the NHS, but for Singapore's model it makes complete sense.