You can be a conscientious objector to the draft, to vaccines in school and the workplace. I don't know your nationality but believe me, America is not built on the premise that the government should inject you with substances against your will so that you can participate in society.
And I say this as an advocate for most vaccines.
There's an important legal and ethical distinction between compulsory vaccination, in which people who refuse are forcibly vaccinated, and mandatory vaccination, in which people who refuse are denied social privileges. In the United States the former has rarely ever occurred. The latter has been upheld by the United States Supreme Court for more than a century (
Jacobson v. Massachusetts; Zucht v. King) and laws mandating vaccination predate that landmark ruling by half a century. There has never been a federal law mandating vaccination in America, but since 1981 all fifty states have had mandatory vaccination legislation, and they are not obligated by federal law to permit non-medical exemptions.
In some states in the earlier part of the 19th century when smallpox epidemics had been savage there were laws requiring town authorities to adopt measures for the vaccination of their inhabitants twice a year, and those who refused to have their children vaccinated were fined. It was expensive to enforce, though, and more cost-effective for towns to simply hire physicians to vaccinate all who wished it for themselves and their children. Laws requiring isolation and quarantine of anyone potentially infected with smallpox
were strictly enforced, which motivated more people to take advantage of the provided vaccine.
Massachusetts passed the first mandatory school vaccination law in 1855. While it protected older kids, it left children younger than school age vulnerable, and hundreds of victims in an 1859 smallpox epidemic were under the age of five. After that there were more attempts at compulsion, but it was never legally permissible to physically restrain any competent adult and inject them.
In the early 1900s the Boston area was besieged by smallpox, and in an effort to exterminate the disease the health board ordered everyone to be vaccinated. Those who refused were fined $5.00. By 1902 nearly half a million people had been vaccinated, and the epidemic ended in 1903. A Lutheran minister who'd immigrated from Sweden refused to be vaccinated, and refused to pay the fine. He was tried and found guilty, but appealed. Eventually it made its way up to the Supreme Court. In 1905 SCOTUS ruled in
Jacobson v. Massachusetts that the right to refuse vaccination wasn't guaranteed by the U.S. Constitution. Writing for the majority, Justice John Marshall Harlan argued that, in the arena of public health, societal good trumped individual freedom. That ruling has never been overturned.
In 1922 officials in San Antonio, Texas expelled a teenager from high school because her parents refused to vaccinate her. Unlike in the previous ruling, the city wasn't ravaged by a smallpox epidemic, and there was not an imminent fear of one. Nevertheless, city officials refused to allow her to remain in their schools without being vaccinated, citing the welfare of the student body. That case also made its way to SCOTUS, and in an unanimous decision it was ruled that the girl's expulsion did not violate her constitutional rights. It was this ruling,
Zucht v. King, that gave states the right to enforce vaccination as they deemed necessary.
In the 1960s and 1970s powerful political families determined to eradicate measles joined efforts. School mandates dramatically decreased outbreaks, to the gratitude of most of the public, but a few were furious that unvaccinated children could be barred from school, and sued the states, claiming protection under the First Amendment. It wasn't
Zucht v. King that was the most influential on the rulings against those suits, or the others that followed in regards to vaccines, it was actually a suit that on its surface was unrelated to vaccination,
Prince v. Massachusetts. The Justice who wrote the majority opinion for that case stated that "the right to practice religion freely does not include liberty to expose the community or the child to communicable disease or the latter to ill health or death. Parents may be free to become martyrs themselves, but it does not follow that they are free, in identical circumstances, to make martyrs of their children."