Can anxiety give you food intolerance?

My partner has an undiagnosed chronic disease that doctors often think is anxiety. One of his symptoms is a growing list of food intolerance.

It's been 10 years now, and he's doing mostly ketogenic diet. Dairy is OK but nuts aren't.

If he eats the wrong food, he gets strong "headache feeling" within 20 minutes, and sometimes he can also get very ill for days for some food. He never gets any stomach pain or digestive problem.

Is anybody here with anxiety having this symptom?