Do they?
I wasn't thinking of the pharmacutical companies, I meant companies that required employees to get vaccinated in order to keep their job.
Can an employer make you take a vaccination that may be harmful to you with no repercussions?
That is the question.
The short answer is yes. Happened to me. I work part-time (pretty much when I feel like it) as an EHS coordinator for a drug compounding company. You could think of it as a mini-pharmaceutical company. Rather than actually manufacture drugs, the company takes already-prepared drugs and compounds them under sterile conditions for health care facilities. Put them into syringes, bags, and other ready-to-go containers.
The interesting thing is, before Covid hit, the company made getting a simple flu shot a condition of employment. I refused to get that shot and told my boss. Also told him I have no medical reason why I refuse to get the flu shot and asked him if he wanted my resignation. He said, nope, you're part-time and work from home about 99% of the time. Yep, that's true, I said.
Sure enough, the HR Manager asked me for proof that I'd gotten the shot. I told her I had not and had talked to my boss about that. The whole matter was dropped. I don't know if anyone was let go as a result of refusing that flu shot -- might've been an empty threat, but they did make it.
The reason I refused to get the flu shot was I was NOT going to allow an employer to tell me what I have to put in my body. I've gotten flu shots before, but it was always my choice - not a requirement.
I'm not an anti-vaxxer. That same employer OFFERED the Covid vaccine (Pfizer) and I took that offer. Was not a requirement. I'm still employed.