If there wasn't an opt-out clause, I'd agree with you. But so long as you can sign yourself OUT of vaccinations, the "mandate" isn't really a mandate, it is just a strongly worded suggestion.
But the issue of whether the state should require ANY vaccinations is separate from whether they should require THIS vaccination.
BTW, as a quasi-libertarian, I am still in favor of vaccination programs, because it IS an area where government has to protect the common good, and only government can do so.
If every other person gets vaccinated, it is in your own interest NOT to be, since you can't get the disease from anybody else and you might be hurt by the vaccine.
But if everybody acts in their own interest, thousands, maybe millions, will die because nobody will get the vaccine.
It is a classic case where government is necessary for society to benefit as a whole where individual greed does not lead to optimal outcomes, or even good outcomes.
It's like having laws about which direction to drive on the street, and speed limits and stop signs. On an individual basis, you could violate all those things from time to time with no harm, but if there were no rules, we'd all be getting our cars fixed.
A parent refused to vaccinate his child and not only was the child banned from the classroom but the school system moved to remove the child from the parents home.
This was a NJ freeper and goes back a few years ago. I do not know how this was resolved.