Indeed, when the government can take away your ability to earn a living, it is communism.
No no no, when you determine that people must be allowed to make a living, that's what is communism.
Unvaccinated people are not entitled to a job without consequence.
If someone doesn't want to get vaccinated, they're very welcome to go work in a job that doesn't require it; I know people that are happily earning a living while unvaccinated. There is no right to be able to work exactly the job you want on your own terms.