What would cause an intolerance to glutamic acid? Gad autoantibodies? Gad deficiency? Glutamate receptor autoantibodies (anti-nmda, anti-ampa)?

None of the above. Msg - ubiquitous Amino Acid and major excitatory neurotransmitter in brain. Studied extensively. Does not cause allergy or intolerance except at high dose and only then in susceptible persons when given in large doses without food. See fda, j. Nutrition, food chem and toxicology, etc.
Diabetes. Anti- gad antibodies are made by your body against your Insulin producing cells. This can result in diabetes type 1 which would require insulin. No ones knows exactly why this happens. Get checked by your doctor. Good health to you.