According to http://www.isbe.state.il.us/bilingual/htmls/imfaqs.html
"The laws of Illinois and the United States guarantee all students in Illinois access to a quality education. This requires every district to guarantee all students equal access to the full range of programs and resources."
"Additionally, the U.S. Supreme Court ruled that undocumented children have the same right as U.S. citizens and permanent residents to receive a free public education."
According to http://education.stateuniversity.com/pages/1882/Constitutional-Requirements-Governing-American-Education.html, the federal Constitution does not guarantee a free public education. Every state, though, has a provision in its constitution (the "education article"), that does guarantee free public education.
"Nevertheless, once a state decides to provide an education to its children, as every state has, the provision of such education must be consistent with other federally guaranteed constitutional rights, such as the Fourteenth Amendment's right to equal protection under the law and the First Amendment's right to the free exercise of, and the nonestablishment of, religion. Therefore, even though the U.S. Constitution does not, in the first instance, require that an education be provided, it nevertheless has had a significant effect on American education."
"Any treatment of education and constitutional rights must begin with the Fourteenth Amendment, which guarantees every citizen equal protection under the law."
So if you have equal protection under the law to attend the public school in your area, no matter what your skin color, sexual orientation, or religion, that right extends to whether or not you have been injected with chemicals or not.
There is no law saying you can't go to school an hour, a day, or a week after receiving a live-virus vaccine, when you might be contagious. There is also no law saying that you can't go to school with the sniffles or a tummy ache, even though you might be coming down with an easily-spread virus, EVEN IF YOU ARE FULLY VACCINATED, and you might be at the height of contagion.
It would clearly be denying someone "equal protection under the law" to prevent a healthy person from attending school because they have not been injected with a chemical cocktail.