The current evidence is that vaccines can reduce the chance of someone getting infected - and thus not give the virus to someone else - by between 60% and 85%. This is based on mass data rather than small scale studies which tend to grab the limelight. Furthermore those with vaccines are less likely to have a severe infection - which puts others more at risk due to coughing and such like - and less like to end up in hospital. And regretably using healthcare is one way this disease spreads, people do catch COVID in healthcare settings. But that 60 to 85% is way short of 100%, hence "breakthrough" infections, entirely the wrong word, still happen.

Now I don't favour harsh treatment to those who are hesitant (but I am quite happy to tell someone unvaccinated that they are being selfish), because actually vaccines isn't just about COVID, it's about a long list of other diseases. Some communities have 90% plus takeup of vaccines without any mandates, people turn up thanks to education, not wanting bad things to happen to them, it's cheaper for everyone, and yes, a bit of peer pressure. Many men need a bit of nagging from the wife to sort out health care issues, and that's good and normal. But that halcyon approach is being undermined by people putting out completely false information. Even worse, is having an anti vax narrative and then picking and choosing the science and pseudo-science to underscore the narative, rather than the other way around. Some of my opinions have had to change because the science evidence has changed. I wasn't terribly keen on Boosters but we can see from the UK death rate it clearly works, so that data changes my narrative. But some people are determined not to let the evidence drive behaviour.