MY opinion is that overdoing anything causes allergies. No this or that until they're one then yay, they had their first birthday now we can give him PBJ sandwiches and egg anything for breakfast & lunch everyday.
I think it's ok if they *occasionally* have the suspect food in *small* amounts (if your family doesnt have any problems with that food, of course) and slowly build up to more.
My personal experience is not food related but I think it's the same principle in how your body reacts to an allergen. When I was young we had a cat. (My only memory of it is me letting it out when it was so insistent on going outside, and that was the last time ever....sad huh?!) Anyway when I was a teen, we went to visit some relatives a few hours away and spent a good long while there visiting. They had 4 Siamese cats in a small apt that wasn't well vacuumed. My dad and I started having trouble with our chest and breathing (I also had the weird sensation of my lower front teeth feeling really cold and hurting). My mom said it was the cats, but I didn't want to believe her. However I had to when while playing with one of the cats, it accidentally scratched my hand and it swelled into a red welt with white right around the scratch. My poor dad was sick for a week after that and both of us have been definitely and clearly allergic to cats ever since. (Same thing happened with sun exposure when we went to the beach with my 6yo sister. She still to this day has to deal with sun/fluorescent light sensitivities as it will make her sick and it is hard to be a mom now when being in certain lights make her sick.)
Principle is- if your body has not had any exposure to X product for a long time, then all of a sudden gets a lot - you betcha your body could react!
So, one year old is NOT a magic age - it is just an age where their little bodies are a little bigger and more able to handle small amounts in their system.
Moderation in all things!
One more thing I wanna add is that when a person has a strong dislike or distaste for a certain item (for my husband it's fish & milk) respect it! I thought my husband just didnt like fish/sea food. but after eating a really delish salmon dinner some dear friends made for us, and then seeing him visiting the 'white porcelain throne' all night long, I understand it was more than just a 'dislike' but his body protecting him from something that his body cannot/does not process very well. Same with milk - he is fine with processed milk, just not cold milk from the jug, he has to have some lactaid with it.
When my son was little he refused to eat peanut butter! (darn, because he needed (still needs!) fattening up!) So when he went to kindergarten a few years ago and had the last lunch shift (they had a morning snack) I did not want to send stuff that needed to be eaten cool/cold. So I used Nutella, and all through the year, I gradually mixed a little more peanut butter into it. Now, he will take straight peanut butter but not everyday.
Sorry this is long!