If the job requires it, okay, but should the job require it? I understand the reason why nurses and teachers would be required - they are more at risk of getting the flu and transmitting it to people who are more vulnerable to it (sick people and children) and who could have more serious consequences if they get the flu. There's a question of public health involved.
Having said that, there should be (and I think there is) an option to waive the requirement, either temporarily or permanently, depending on the circumstances.
My mother works in a pre-school and had to start getting the flu shot. One year, she started feeling numbness in her hands and feet. Didn't know what caused it. The next year, right after she had the flu shot, she ended up in the hospital with Guillain-Barre, an auto-immune syndrome. The body attacks the peripheral nervous system. And yes, it can be the result of a reaction to the flu shot.
She doesn't get the shot anymore and her job waives her requirement to do so. And because there's still a question about whether or not this kind of reaction is hereditary, I don't get the flu shot either. (To be honest, I never got a flu shot before that, either.)