All is not lost you can use ground flax seed in baked goods. Used it when I had no eggs for pumpkin pie
Oh and there is vegan mayo.
I wonder if it’s just chicken eggs, wonder if duck eggs would be a problem or any other poultry.
I am “allergic” to tree nuts, especially almonds, but I can drink almond milk and eat pasteurized almonds with no problem.
Husband is wondering if it’s something the chickens are eating, like soy. Look into soy and corn free fed for your chickens before getting rid of the chickens