I'm not a lawyer, but if I'm reading that link correctly, while the COVID vaccine is indeed mandatory (good), the flu vaccine is opt-out. It seems participation in the two vaccination programs is required, but in case of influenza vaccination, I think it's saying that opting out explicitly constitutes participation in the program (basically meaning that you can't just ignore the program and need to either vaccinate or inform them that you won't).

The email seems to be more strongly worded than warranted, if my interpretation is right.