Abba:
You wrote: “The state can’t force them to vaccinate if they claim they are not doing it for religious purposes. ”
Stop it. You are out of line according to Torah by insisting that it is a religious issue when it is not. Is it a mitzvah to drive a Toyota? You might feel it is unacceptable for the dealer to charge you so much for a new car that is outside of your range. and that he is denying you the right to own a car, as if there is some sort of Torah obligation to provide you with one.
Whatever my opinion about vaxxing is, you are blasphemous to claim that you have a Torah given privilege to make that choice.
Take it from the Gedolim: There is ZERO basis in Torah to avoid vaxxing. It may your preference. But there is NO religious exemption here.