I understand your anger and agree that anti-vaxxers are stupid. I believe public health education should be part of the school system.
I also agree that it’s responsible for a society to impose reasonable restrictions on members that endanger it.
I think people do have an ethical obligation to take reasonable precautions avoid potentially exposing others to pathogens. Vaccination is an example of reasonable precaution. People have the right to bodily autonomy, do not vaccinate them against their wishes.
I do not support the firing of workers for refusing vaccinations if they can do their job remotely. People shouldn’t have to decide between their religious beliefs and employment if their employment doesn’t bring them into contact with others. (Imo anti-vaxx is essentially a religion, this may say more about my beliefs regarding religion than about anti-vaxx sentiment).
By all means exclude the unvaccinated from places where they can be reasonably understood to endanger the public, or others that have a similar right to be there.