There are no accepted diagnostic criteria for autoimmune disease resulting from vaccination. Autoimmune diseases develop a long time after vaccination, and because of this, it is hard to conclude of a causal relationship. Vaccines contain adjuvants, preservatives, antigens and other ingredients, each of which can cause or exacerbate autoimmune reactions.
The authors vaccinated 40 children against hepatitis A, and 25% of them developed autoantibodies (antibodies to own antigens), and one of them developed a temporary leukopenia (a decrease in the number of white blood cells). Two years after the vaccine, two children still had autoantibodies.
Those who did not have measles in their childhood (or had a sick atypical, without a rash, like after vaccination) had an increased risk in adulthood: 1) immunoreactive diseases (autoimmune diseases due to an infectious disease),
2) skin diseases (dermatitis, eczema, etc.),
3) degenerative bone and cartilage disease (osteoarthritis, etc.),
4) oncological diseases.
If some vaccine component is similar to a protein produced by the body itself, then once the immune system learns how to react to the vaccine protein, it may also learn to react to its own protein (the one similar to the vaccine protein) in the same way. This is how one gets autoimmune disease. This phenomenon is called molecular mimicry.
This article explains the mechanism of molecular mimicry between tetanus toxoid and IgE receptor, which is probably what leads to an increased risk of allergies in vaccinated people.