Let’s look at that. Employers and demand employees to get, say a flu vaccine. Or an employer can demand that an employee buy (or use safety equipment. In the first instance the employer is protecting their clients (patients) from exposure to a virus that might cause them harm. In the second instance the employer is trying to protect themselves from being sued by the employee for not protecting them from some hazard. In case number one the patient has no control over what they are being exposed to, and I would argue the the employer has the right to demand the the employee get vaccinated. In the second instance the employee knows the risks and if he/she elects to take that risk it is their responsibility. they should be made to sign a waver but after that their on their own.
Either way there is a potential for being sued if the employee fails to comply and either infects co-workers or neglects to purchase and wear safety shoes.
Reasonable requirements I don't have a problem with purchasing. Vaccinations, I would still want to refuse. It all would come down to how badly I want to keep my job.
I have all my childhood vaccinations and before I had a chance to refuse I got a booster tetanus shot. I saw to it my children received all their vaccinations while they were in my care. To some extent I've let myself get spooked by the anti-vax crowd. And my chiropractic cousin turned to homeopathy, also my chiropractic neighbor whose kids were healthy as horses and were not allowed to receive vaccinations. So my daughter and I talk about it in front of my grandson who told his school that I didn't believe in vaccinations (which isn't totally true but let the school think what they want about me, I don't care, I'm not his guardian). My daughter asks me if she should let him get one. I said it is not fair of me to influence you, I will not say, you do what you think is right. So he got it. You can refuse in our schools but it will be more and more trouble for people to do so.
I think I did mention to my daughter that if she refused her son permission to get a vaccination, the school would probably make trouble for her.