Millions of people in various sectors outside healthcare (by the way, since when is healthcare a "small sector"?) have had vaccines required as a condition of employment. , mostly people with plenty of risk like teachers, the military and some people working in the travel industry, but this is not always the case. I was required to get the flu shot (or an exemption) in my last job at an electrical engineering firm.
On a broader note, I think (coming from the US) workers should have stronger protections against being fired, but everyone I've personally talked to who does not believe your employer should be able to fire you for not getting a vaccine is also opposed to "state controlled employment" or almost anything else that exerts control over the employer-employee relationship. You can be fired for almost any reason in the US, being fired for not getting a vaccine does not seem any worse to me than being fired for any number of awful yet totally legal reasons.