I think the work case is the weakest possible. You're not owed a job, and you're certainly not owed a specific job. The reality is that vaccinations don't just affect you. They affect people who aren't physically capable of being vaccinated (compromised immunity, allergy to vaccine, etc.). If you bring the ratio down below the herd immunity threshold, you can spread serious diseases to those not physically capable of being vaccinated and putting my existing employees at risk.
If I, as an employer, am forced to decide between hiring you, an antivaxxer, which risks killing even one of my existing employees, you're not getting the job, period. I owe them a duty of care before you. And their families too. And babies too young to immunize -- is it okay if they die?
This stems from a similar misunderstanding of liberty as the "freedom of speech applies to Twitter" argument. The first amendment protects you from legislation infringing on your free speech. It doesn't require private companies to broadcast your speech at your sole discretion. The same would be true of a hypothetical vaccination rule. Even if the government weren't able to legislate in this regard, nothing precludes any private party from refusing you food, a home or a job on the basis of your vaccination status. Being an antivaxxer isn't a protected class to the best of my knowledge.