It would be better if we had an education program that resulted in herd-immunity vaccination levels instead of mandated compliance. I support vaccine mandates for school staff and any individuals eligible for vaccination because we need to place the needs and safety of the many, and the most vulnerable, above the wishes of the individual while our community risk is high. The goal of such a mandate is not to fire the uncompliant, but to work with people to provide the best information and educate people on this so that they choose this protection for themselves and their families. There are many activities that are not allowed in schools and people accept this as part of the social contract. Reducing our chances of carrying extremely infectious materials into our schools is an acceptable requirement.
I recognize that some individuals may have legitimate reasons that a vaccination is not viable for them (removed your examples) in these cases I would support alternate arrangements like rapid testing while ensuring that alternatives do not place others in any greater risk. I am in a workplace where vaccination is required and this allows us to carry on activities we could not otherwise. In schools, we want to offer varied programs, music, singing, sports and extra-curricular activities. Vaccination is one tool among many that allows this to happen.