It's my opinion that if someone chooses to work in a healthcare environment (hospital, medical or dental clinic, nursing home or other long-term care facility) where there will be so much interaction with other people, YES, he or she should be required to receive a flu shot every year unless allergy to eggs (used for producing vaccine) can be proven.
There is so much misinformation about flu vaccines, and I can't tell you how many people I've heard insisting that that they don't get the vaccine because, "...it gives me the flu." NO, IT DOESN'T! Some people do have a very minor reaction that is equivalent to a light cold, but speaking as someone who nearly died with the type of influenza that has killed many people (think back to the 1918 pandemic that decimated families, which could happen again with some of the newer flu strains), it's pure rubbish to claim the flu shot gives anyone fullblown flu. It just does not do that, and using a mild reaction as an excuse not to get an injection is just that--an excuse.
I get the flu shot every year since the last time I missed getting it (13 years ago) and was subsequently incredibly sick with "real" flu. True influenza makes one so ill it's almost impossible to move. The entire body aches severely, there is high fever and usually a cough that lingers. The sufferer is so ill that he or she may become dehydrated or, if living alone, not be taken care of properly. It's really dangerous for the elderly, very small children and anyone with a compromised immune system.
By the way, this year there are two vaccines, one of which packs a double punch against more than one type of flu strain. I asked for it, got it and couldn't even tell I'd had the injection. Not even a bit of soreness at the injection site.
So I think that any healthcare worker who doesn't want to get the flu vaccine is selfish and not really dedicated to healthcare. (By the way, I'm of the opinion that anyone who works in the healthcare field strictly for a job and paycheck, and not because he or she really cares about taking care of the sick, does not belong there!) I can say this because I know many doctors, nurses and other healthcare personnel who are truly dedicated and show it every day. (I've also met more than my share of the other type, unfortunately, three of whom were arrogant surgeons who left me in worse condition than they found me. That's another reason I wish the U.S. had a national healthcare service so that people like that didn't choose the profession just to get wealthy and gain prestige. That's why there are too many of this latter type--usually surgeons or other specialists, although I've known some very dedicated surgeons and specialists as well. It depends on the individual, as do most issues.) Sorry I got on my soapbox and got carried away!