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.
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.