Allergies
Azo food dyes do not cause allergic reactions as such. Many azo textile dyes can cause skin hypersensitivity and allergy, but these are not used as food dyes.
Azo dyes are too small to have a direct effect on the immune system and thus do not cause a direct allergic reaction. However, some azo dyes, especially tartrazine, may increase allergic reactions towards other substances (among these many drugs). Similarly tartrazine (and probably some other azo dyes) may cause increased symptoms in people with asthma and similar disorders.
The exact mechanism why tartrazine increases allergic reactions or asthma is still not fully understood.