Your ideology posits that whatever you deem to be "good for society" gives you the justification of using violence to enforce. First I'd like to point out that there hasn't been a tyrant known to the face of the earth who didn't use such rationalizations. But secondly, it is worth noting that implicit in this claim is the presumption that everyone is your slave, and everyone's life is to be lived according to your (or your creed's) edicts.

Of course every tyrant used such "rationalizations"--every governing institution in the history of man explicitly initiates force and infringes upon individual freedom in favor of the common good, and we have things like taxes, freeways, and food inspections to show for it. The kind of libertarian objection you mention isn't just an objection to especially oppressive government--it's an objection against all government.

This isn't a straw man attack, either. If you don't allow for some amount of initiative force for the common good, you don't allow for any system of government which has ever existed, including the US Constitution. Consistent libertarianism leads to anarchism. And that's why the force card isn't effective: it's the logical equivalent of saying "the government shouldn't mandate vaccination, because the government shouldn't exist".

The only two logical options are to be an anarchist, or to concede that some violence for the common good is justified--and then go on to discuss why this instance does or does not justify institutional state violence.

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On the other hand, negligently infecting other people with communicable diseases is a form of physical force, and hence there is a legitimate interest in preventing this from happening.

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Finally, what you're discussing is ideology. Now, it's important to point something out. There is an important distinction between science and "ideology", or whatever you want to call about it, in that science is only concerned with matters of fact. Matters of value and morality are explicitly outside of science. The closest science can possibly come to ideology is when the facts would dictate any sane person to choose one option over the other. For instance, if scientists tell us they are 99.99% certain that an asteroid will collide into the Earth 20 years from now, and that in the event of a collision, it is 99.99% likely the human race will immediately go extinct, any sane person would conclude "we have to do something to stop that astroid". But science, qua science, can't come to that conclusion by itself. If you were some type of madman who wanted to destroy all human life on Earth, the science would be just as interesting and convincing to you as it would be to a sane person, you would just be led to a different reaction due to your value system.

Or, back to this point--if your value system favors children not dying preventable deaths from 19th century diseases, you probably favor vaccination. But if your value system favors not being forced to do things against your will over children not dying preventable deaths from 19th century diseases, that's entirely up to you--just as long as you accept the facts of the situation.

And, historically, this is what a lot of anti-vax people fail to do. People aren't rational enough to just say "I value not being forced to vaccinate my kids over my kids' lives" (which is a disgusting value system, but you can't argue against value systems), they'd rather lie about facts and say "vaccines cause autism, therefore it's in the best interests of my child not to vaccinate them".