The scientific method is practiced by imperfect people with biases and external motivators. That is why thorough peer review is required (and sadly lacking).
Look, I didn't get vaccinated because I was told to by pharmaceutical companies. Those shady bastards are on TV all the time selling stuff that seems super sketchy.
ALSO, I didn't get vaccinated because I was told to by doctors; I've had enough experiences with them getting things wrong in what they tell you to do.
I got vaccinated because doctors and health professionals THEMSELVES got vaccinated without hesitation. Was lucky enough to see a good friend, a quasi-famous black doctor, get the jab on TV, which sealed it pretty quickly for me.
AFAICT, there aren't. Very small numbers have left (permanently or temporarily) jobs for that reason, whether fired, quit, or suspended. On the order of hundreds out of ~17 million health care workers covered by mandates.
Lots of political opponents have pointed to mass firings as hypothetical future consequences of mandate policies, and then reacted as if these hypothetical future outcomes were present reality.
There are 17 million employees in the healthcare industry as a whole, but so far it's a handful of healthcare systems that have announced this firing policy, primarily (but not exclusively) in NY and California, and an even smaller subset has actually gone through with firing people. Of course, even 1% of 17 million healthcare workers is 170,000 people, and even if 95% are vaccinated, that's still 8,500 people to be fired. And 95% is optimistic.
As to the claim that only hundreds have been fired, I'm not sure where you are getting your data. One healthcare provider in NY fired 1400 people[1]. 87% of New York's hospital workers are vaccinated and 64% of New York's general population are vaccinated.
So if the providers in extremely blue areas are faced with firing 13% of their healthcare workers, I'm a little skeptical that only hundreds will be fired, or that this is even a workable plan. But who knows, I don't think anyone has the full count for the nation at the moment. If you didn't just make it up, then please do share your source. More facts and less speculation are needed when discussing this issue.
[1] https://www.axios.com/new-york-northwell-health-vaccine-mand...
As of Sep. 28, CBN could find only 843. And, oh, look, they linked to https://www.fiercehealthcare.com/hospitals/how-many-employee...
Kaiser Permanente and Northwell Health were the largest with 1-2% of their workforces, although Kaiser's are on "administrative leave".
Also, some of these stats include nurses that are still registered but not currently working anywhere so it's unclear that their vaccination status is correctly recorded.
But right now you must be in one of the two fields: you are either an anti-vaxxer or you believe in science and will do everything your government says. There are no room for rational discussion about important issues anymore. You just choose your team and fight for it till death.
It opens up for these fringe movements is to present themselves as scientific, since they too have papers they can point to, and arguments that mirror the form of the scientific establishment.
The way to beat them is to be very clear about the limitations of science, and stop trying to misrepresent it as having a larger degree of certainty than it has. Science is demonstrably wrong sometimes, especially early research like the stuff that was circulating in the beginning of the C19-pandemic, and to make matters worse, a large part of science is dedicated to identifying instances where science is wrong.
That clashes with the official message is "trust the science" and makes devastating ammunition for undermining its credibility, especially nowadays when it is very easy to go back and check what claims were made in the past against which claims are made today.