This is where I am.
If you can't win the argument based on the science, you won't win it by linking state power with science.
Why?
Because as a rule science is a trusted field whereas trust in the state is much lower. If you mix the two science loses.
In terms of the demographics of unvaccinated, you see patterns with income. The least deprived are generally the best educated and have best health outcomes and access to health and have the highest vaccine uptake. The most deprived have barriers to health care access and lower understanding of the importance of vaccines.
We also see cultural patterns. London has much lower uptakes than other parts of the country. This is a worry for obvious reasons. The difference is largely due to imported views about vaccines from countries which culturally have less trust in both science and the state and have more disinformation.
The most interesting thing in the uk is the lack of mainstream politicians who have an anti vaxx agenda. It just doesn't exist. Its not tolerated and its not wanted. Its just not a thing. This isn't the case in other countries. But there is still a certain fragility - anti-vaxx influencers for covid were traced online. The messages in Germany were attributed to about a dozen people worldwide, but these voices had been amplified in a very distorted fashion by social media. There are real concerns about algorithms on this.
It is important for us to examine what we know works in terms of vaccine uptake and what doesnt in a scientific way. Just as much as we follow the science over vaccines themselves.
And that shows that mandatory vaccines do not work.
Indeed by excluding children from mainstream education and child care settings for vaccine status, you might be setting up for other problems. A parent who doesn't want to listen to vaccine messages, is more likely to have been influenced by dubious internet or cultural messages - which can harm. So what other harms might a child be exposed to? That child is outside normal child protection eyesight. The child has rights to be protected even if they aren't vaccinated. And these risks are higher than the risks of being unvaccinated. We need to calculate this into our thinking on mandatory vaccination. Unvaxxed kids dont have a choice; every bit as much as immunocomprised kids don't have a choice. Who is more important - neither - we have to balance the rights and safety of the two. Hence why certain diseases are notifiable in the first place and schools have the discretion to inform and excuse immunocomprised kids from school if necessary on health grounds if there is an outbreak.
Ironically not mandating vaccines may protect immunocomprised kids more than mandating them if it increases the uptake and level of herd immunity. Which may seem perverse but is the statistical reality.
Information campaigns in low uptake communities and trust building with health care providers is a much more effective way of increasing uptake than mandating. Its more time-consuming and costly but it works. Unlike mandating.
As for the anti-vaxxers on this thread. In terms of changing minds its proven better to engage by exploring individual reasons for not taking up and unpicking them in a calm and rational way. Chastising and being confrontational is known to have the opposite effect as it entrenches, alienates and others. It becomes them v us rather than examining reasons and debunking myths in a supportive way.
If you talk to those who didn't take up covid vaccinations, you get a surprising range of common patterns - accessibility to health care, cultural and family pressures not to (including controlling behaviour from a family member), fear of needles and/or hcp (specialist clinics which advertise they are supportive of these needs have been really effective), family histories of reactions to vaccines (not all vaccines are the same and there are sometimes alternatives - its worth exploring the science and differences on this one to one - or offering extra monitoring after a vaccine) and then theres the general disinformation which just needs good quality discussion and trust building.
So my question to the OP would always be why EXACTLY don't they want vaccines and would be to say to others to listen, take time, stay calm and rational and then debunk. Leave any emotional input or feelings at the door and stick to the science. The science wins these type of arguments on merit for a reason.
And the reality is there will always be a percentage of the population who will avoid vaccines on non medical grounds even if you mandate it. So don't think that 100% vaccine rates are achievable. I'd personally argue that 100% vaccine rates are not actually desirable given what that means for consent anyway.