This young man can't eat a thing without first knowing exactly what the ingredients are. He's been to the hospital multiple times due to accidents.
Which means his health issues are incompatible with military service.
He is not going to be able to know the exact ingredients to the food served on ships, chow halls or in MREs. This is especially true in a deployed, field or combat situation. The Navy is not going to accept someone that has this type of problem. It's an impossible situation. He'd couldn't be deployed or sent to sea.
Even if by some chance the Navy would accept him, is it really fair to those he's serving with? I'd hate to be flying with him knowing a crew meal could kill him or incapacitate him. What about the Sailors depending on his leadership during a crisis but an allergic reaction is crippling him?
It might be his desire, but it's not a practical desire. It's not safe for him or those around him.
This is probably why the officer recruiter is not investing his time on him. Part of his job is determining the suitability of any candidate. I would not recommend someone like this for any military job even if he could get a waiver for the medical condition. I wouldn't be able to sleep at night if I did. It's not fair or safe to the applicant, those who serve with him or to the Navy in general.
Not what you want to read, but someone needs to put out the cold, hard facts. A life threatening food allergy is not compatible with military service. Especially with an allergy to a common product used in so many foods.