Each state Constitution is different. For instance, there's nothing in the Texas Constitution that deprives it of requiring vaccinations for state funded facilities. As Madison said, the powers of the Federal Government are few and defined. Those which are to remain in the State governments are numerous and indefinite.
I also don't see anything in the Constitution requiring compulsory education in a public school, which is not something I'm advocating, and is irrelevant to the topic.
Keep your kids home for all I care.
Why golly gosh, another response from you that does not address the question asked. You failed to cite a part of the Constitution that compels vaccination or compulsory education/government education. All 50 states allow homeschooling, just so next time you are not so ignorant. If there is not a State funded facility required for all per your post there is not a State requirement for vaccination.
Previously you stated "State governments are well within their Constitutional authority to require basic health and safety measures for the 50 million children who attend public school. You're perfectly within your right to leave your children defenseless against deadly diseases, but you cannot pass that risk on to other children. That isn't liberty."
My children attend a government school; and within their rights they have refused vaccines. Not only are they able to pass that risk on to other children(who evidently are not immunized despite being vaccinated...screw science and how immunization works) they can and do. On the positive side I am glad you have shown yourself for the liberal that you are since you are clearly advocating more power to governments than the law allows and being ignorant of the current state of our laws.