As George Washington himself did.
Whose rights are greater?
No one's "rights are greater." This is a false dichotomy. Does the government have a right to force people to take the flu shot? No. If a flu came along that was so deadly that the government wanted to force people to get the flu shot, then the government would need to prove the necessity and the spread-prevention efficacy of that medical procedure.
If you're talking about the United States, this question has been settled at the federal level by the Supreme Court for over a century. At the state level, the first vaccine mandate was in 1809. Most states have vaccine mandates for children, many of them with only medical exemptions. It's legal. It's not some great infringement on your rights.
Right, the Federal government does not have the right to force the public to take a shot, while states may. It may appear that public health is being run at the national level, but really the CDC issues recommendations and many states ignore these recommendations and replace them with their own. Public health is run by the states, but that doesn't mean the state can do whatever it wants. Each state has its own constitution, and its own state supreme court that verifies whether any mandate is lawful, so this is going to depend on the state constitution and local public health laws.
The fact that the treatment varies state by state shows that people do consider this to be a right worth retaining, and in high enough populations to hold sway over local Government up to the state level.
Yes, we live in an age of mass-indoctrination. If Fox News runs Anti-Food Safety segments 24/7 for months, we're probably going to have a few states that remove punishment/fines/laws for people who prepare food with shit on their hands. That doesn't mean that serving food with shit in it is an inalienable right.
* Quarantines have been used since the middle ages and they were used against people showing symptoms or groups of people likely to have the disease. We haven't had quarantines with covid. We've shut down society as a whole.
Vaccines, even when not fully effective, greatly reduce the amount of virus you shed, and thus significantly reduce transmission.
Anecdotes are near-worthless, but I will share that my neighbor got covid. He was vaccinated and boosted. His wife and him felt sick, as did their infant (obviously not vaccinated), for two days. TWO DAYS ONLY. ...and their other two children never contracted it at all - tested negative twice each.
Getting vaccinated reduces disease severity AND transmission.
The Covid vaccines are fraudulent and more and more people are realising this. The CDC changing the definition of a vaccine from "providing immunity" to "increasing protection" just after Covid-vaccinated people started getting infected shows arm-in-arm corruption with big pharma.
Your 10th booster shot will kill you not save you.