I am a big supporter of public health measures. People working in public health settings such as hospitals, and medical clinics, etc are on the front lines of infection for all kinds of stuff. They are essentially vectors because of their wide exposure to sick people. Because of this, I believe that every measure that has been shown to be effective and safe should be employed to stop infectious transmission before it starts and the obvious place to halt the infection train is at the depot, hospitals, medical clinics and doctor's offices. If you go to a hospital or clinic you should not be increasing your chances of getting sick with preventable illness.
To address some of the points raised: Egg allergy is no longer an excuse, there are now vaccines produced without eggs, the article I linked to mentions this. Public health officials do sometimes get their predictions wrong and immunize against the wrong strain of virus, in that case the whole population is at risk and it is a major fuck up but shit happens, and I don't see this objection as an excuse to forgo vaccination. Vaccines are not 100% effective, but, again I don't see this as a valid excuse. It is certainly true that some people will react badly to a vaccine, and some will die from it but far more will die from the flu or its secondary infections, so the best course is to get vaccinated.
The most puzzling thing to me is that a nurse would refuse vaccination. The greatest leap forward in public health, after simple hand washing, is vaccination.
So, I support the actions of the hospital in this case.