Given that mammals have been dining on eggs pretty much their entire evolutionary history, and given that we're omnivorous mammals like those early mammals, I'd be very surprised if we developed an immune response to such a good food source. That would be totally counterproductive. I can imagine that a few people out there have allergies to eggs, but I can't imagine we're talking anything other than small percentages (hundreths of a percent of the population).
And I think Jinx posted this before about eating the same foods everyday--and like last time, I'll point out that most people in the world eat the same things most everyday. Most people in Asia eat rice everyday, with every meal--no rice allergies. Most people in Mexico (and the US for that matter) eat corn everyday with every meal and don't have allergies. Most people in Europe (and the US) eat wheat everyday and don't have allergies. Since the switch from hunter-gatherer diets most people around most of the world have not had the luxury of varied diets. We know from several lines of evidence that the switch to agriculture was strongly selective on human populations (that is, people not adapted to eating a few staple crops everyday died). Most of us are descendents of people who farmed a few staple crops and ate them all the time (and people who probably subsisted on pretty bad, malnourished diets at that). So we're adapted to eat the same thing everyday. Some people aren't--they have some mutation and their bodies freak out if they eat eggs everyday. But this is not a mutation that is widespread in the population or everyone on here would be complaining about egg allergies.
Now if you want to talk about allergies to GMO foods--sure, I can buy that. If your eggs are expressing some insect protein or a protein from some funky plant or bacteria, yeah, your immune system might go haywire.