We have that covered in my country.

You can refuse to be vaccinate. No need to justify; your choice, you're cool.

However...

If you opt for not vaccinate your children, then your children can not go to school. Any school. And although you can homeschool, nevertheless you are required to have your children enroled at your local school, in order for them to have formal evaluations and follow ups. But because the children are not vaccinated they don't meet the requirements to enroll at a school, as they pose a threat to other children by possibly carrying diseases with high contagion risk.

And if your children don't go to school, you're criminally responsible for it, as it is considered gross negligence.

So...

And getting a medical exemption is a very hard task, as the medical professional attesting it is mandated by law to prove why a child or individual can not be vaccinated. If demonstrated false, if gets very ugly for the physician.

Religious exemptions don't go very far here. Even JWs can't do a thing if one is carried to an hospital in a life or death situation and doctors need to admnister blood or plasma: saving a life comes first. And if they refuse life saving procedures, they do it at their own responsability and are required to sign a term of responsability.

The logic here, boiled down, is: do whatever you want with your life, as long you do not trample others.

And it works.