Chicken DNA wasn't put into tomatoes, to my knowledge (fish DNA, sure--it produced an antifreeze protein, but never made it to market). But let's assume chicken DNA was inserted.
A chicken contains many 10s of thousands of proteins. The usual allergen in chicken is a blood serum albumin variant specific to chickens. (It's different in turkeys, and much different in mammals, but we all have some sort of blood serum albumin). So if you're allergic to chicken, you're almost certainly not allergic to the cell walls or antibodies or enzymes or lots of other things. Just chicken blood serum albumin.
Putting the DNA for chicken blood serum albumin into tomatoes would be bad. But the other proteins ... Meh.
For shrimp, it's mostly tropomyosin that triggers allergies. If any other shrimp protein were inserted into, say, chickens, it wouldn't be a problem.
Now, they GMO for specific traits. Drought tolerance, production of a vitamin, insensitivity to some mineral, increased cold tolerance, more even ripening. It's unlikely that they'd pick an allergy-inducing protein just given the probabilities involved. The human body has perhaps 50k proteins (and can produce far more). E. coli, a bacterium, has 3000 different proteins.
If they did put in an allergy-inducing protein in a common food, several scenarios are likely. The first is that since they're adding DNA, the product would fail FDA approval without labeling. The second is that the producers and sellers would use labeling simply because they'd have such incredible civil liability otherwise their lawyers would push the scientists and management folk out of the highest window they could find. The third is the news media attention that such a company would garner within days of the product going on the market.
All that's left is fear and suspicion based on not understanding how the tech works.
An aside on vegan diets. It's really hard to know what to make of that particular claim. It's not the protein per say that most vegans object to, IMO, but on the fact that an animal is killed to produce the food. I've known vegans who avoid leather and anything produced from animal because it requires the death of an animal. Put a bacteria or cow gene in okra and no animal dies when you harvest the pod. It's even more removed from what most vegans I've known were concerned about than, say, vat-grown beef (https://en.wikipedia.org/wiki/Cultured_meat#First_public_trial). I guess some religious vegans might. Then again, I'm not sure how I'd feel about a shrimp-protein-containing parsley for Passover.
Naturally occurring urea is largely derived from animals. It's a great fertilizer and used in plastics. Most urea used today is artificially produced (it's the chemical that started unraveling the idea that naturally occurring organic molecules have some special "force" or "power"
. I've known few vegans who reject urea-based fertilizer, whether natural or artificial.