Having seen so much in the news about this, and several excellent post here (including one about the problem of using executive order for this issue that I would link if I could still find it) I think it worth mentioning another serious problem with the vaccine requirement.
In Cruzan v. Director, Missouri Department of Health, 497 U.S. 261 (1990), the U.S. Supreme Court established that the right to refuse medical treatment was a fundamental one. This means that in order to force you (assuming you are a legally competent adult) to receive medical treatment (like a vaccine) the state has to show a compelling interest and that there is no less oppressive way to achieve that interest.
Early on, the Supreme Court ruled that mandatory vaccinations were legal, interestingly this was before Cruzan and they have never applied the compelling interest/least restrictive means test to a vaccine case.
By their own ruling they should, so what would happen if they did,
Note: I am an attorney not a doctor, the numbers I use are my best recollection of the disease risk they may be off a bit, please look at the overall point.
Let's start with one of the first widespread vaccines and one of the ones that the S.C. said could be mandated, smallpox.
Smallpox was highly contagious from casual contact and had a 30% fatality rate if you caught it. So lets say for the sake of argument that you has only a 15% chance of catching it. That still left you with an overall risk of 2% of dying from it, so the vaccine could kill 1% of those who got it and it was still a good bet to get the vaccine.
On to the legal part. The governments interest was in preventing other people from catching smallpox from you and dying (a government interest in saving you life means nothing in this analysis because you have the right to refuse lifesaving medical treatment). When you consider that anyone you came into contact with while infected had a significant chance (10% or more) of getting the disease from you and dying that is a pretty compelling interest on the part of the government. Since nothing other than the vaccine could significantly reduce this risk the least restrictive test is also met.
Courts have since pretty much just said that the S.C. said vaccines could be mandated, but is that really what they said.
HPV is sexually transmitted, that means that if you are lifetime celibate or you and your partner are lifetime monogamous you have 0% (absent blood transfusion and other statistically insignificant risk) chance of catching it, if you are sexually active with a variety of partners your risk of catching it are in line with smallpox. However that is where the similarity ends. HPV (or certain types of it) cause penile and cervical cancer. Not everyone with HPV gets cancer. The fatality rate depends on when it is caught, from 1% for early detection to 85% if not caught until late. Assuming a man pays reasonable attention to changes in his penis and a woman gets regular PAP tests, the fatality rate should be well below 5% and that is of those who get cancer from HPV not just of those who get HPV
The legal part. The government has a compelling interest in protecting me from a 30% fatality risk from catching a disease from casual contact with you. But what about a less than 5% risk of fatality from catching a disease from having sex with you. Obviously a very different question. You can eliminate the risk almost entirely by being selective of sexual partners, using condoms, and being screened regularly. Quite a different story than dying from smallpox because you took the bus next to the wrong person. Even if it is a compelling interest (and likely would be found not to be) the government could protect other people from getting HPV from you and getting cancer and dying through measures like encouraging safer sexual practices or (gasp socialism) offering free screening or other public education and health measures that do not infringe upon your right to refuse medical treatment.
Not that I want to single out HPV, it is the one that has now come up in the presidential election and I think it illustrates the point very well. My point is more that mandating vaccines (or saying anything about vaccines as a blanket statement) is problematic.
Vaccines are a risk versus risk analysis. Proof that a few children were mentally handicapped by the smallpox vaccine may not have been enough legally, or socially, to make us take a second look at requiring it in light of the enormousness of the risk of the disease.
However, with each new vaccine we need to look at how bad the disease being treated is in order to know how much suffering and death, on the part of a few who suffer adverse reactions, we are ethically and legally willing and able to tolerate in exchange for the suffering and death the vaccines are designed to prevent.