I have cared for children with life threatening allergies but they have developed these allergies once in my daycare and so I have worked with the child and their family to accommodate them. However, through those experiences, I no longer knowingly take on a child with life threatening allergies as its not so much whether I can accommodate them and more about not having ultimate control over what is brought into my house by other parents. There are so many parents who feed their kids peanut butter for breakfast and we all know how difficult it is to clean up. my dck's come most days with some remnants of breakfast on their face or in their hair.
As for intolerances although not life threatening should still be taken as seriously because cross contamination can cause illness. Eggs and dairy are easy to eliminate. I had a child with a life threatening allergy to dairy and it was never a problem to accommodate. If you serve processed foods then egg is commonly used as a glaze or binding agent so I would read ingredients for that but if you cook from scratch then their shouldn't be an issue. Soy would be my concern. It is used as a filler in meat products already so you would have to be sure the meat you were buying was abf and hormone free to ensure that their were no fillers. Soy is hidden in baked goods, crackers and dairy so be super careful to research additional terminology used in ingredient lists for Soy.