The more logical theory (and the one with more evidence) is that vaccines cause autoimmune diseases via adjuvants and “non-active” ingredients.

For example, most killed virus vaccines contain an adjuvant like aluminum of thimerosal (mercury). Adjuvants irritate the immune system since your body will not react to a dead virus.

However, your body is just as likely to attack other ingredients in the vaccine.

Vaccines grown in eggs lead to egg allergies.

Vaccines with latex contamination lead to latex allergies.

Vaccines using peanut oil or byproducts lead to peanut allergies.

Vaccines containing squalene (found in plants and the human body) caused desert storm syndrome.

Vaccines containing human fetal tissue leads to autoimmune disease.

Here is one source of many:

https://www.amazon.com/Peanut-Allergy-Epidemic-Whats-Causing/dp/1616082739

Except from a review:

Many vaccine use peanut oil as an adjuvant. When a study was done on this practice was done in the early '70s, Congress' response was to pass a law in 1973 permitting vaccine companies to not put "inactive" ingredients on the vaccine packages, calling their formulas secret and proprietary, never mind that they were killing and disabling many thousands. The peanut oil in vaccines sensitizes many to peanut protein, resulting in peanut allergies on later exposure to peanuts, with sometimes fatal results. Frasier includes statistics on exactly how quickly peanut allergies in the US exploded: in the wake of the Hib vaccine being put on the universal vaccine schedule in 1987, the incidence of peanut allergy increased three times in only three years. This is an aside, no included in this book: Israel has very few peanut allergies, because the vaccines manufactured there do not use peanut oil, but rather sesame oil, so they have a lot of sesame allergies in their children.