Autoimmune thyroiditis, called Autoimmune thyroid disease (AITD), includes forms of hypo- and hyperthyroidism caused by autoimmune attack on the thyroid gland. Hashimoto's thyroiditis is associated with hypothyroidism (underactive thyroid), while Graves' disease is associated with hyperthyroidism (overactive thyroid; risk of thyrotoxicosis).
According to Wikipedia's Hypothyroidism page (as of July 22, 2017), autoimmune thyroiditis is associated with other immune-mediated diseases such as diabetes mellitus type 1, pernicious anemia (Vitamin B12 deficiency), myasthenia gravis, celiac disease, rheumatoid arthritis and systemic lupus erythematosus (SLE or Lupus). It may occur as part of autoimmune polyendocrine syndrome (type 1 and type 2).
[PMID 20604685] This 2010 article provided an overview of the genetic variants involved in autoimmune thyroiditis. Polymorphisms in many genes play contributing roles: HLA-DR, CTLA4, CD40, PTPN22, Regulatory T-cells genes ("Treg", including FOXP3, and CD25), and Thyroid-specific genes (Thyroglobulin, and TSHR gene). They then raised the question, "How many susceptibility genes are needed to develop AITD?" At the time of writing, only one HLA-DR gene polymorphism was highly predictive of Graves' disease with an OR of >5 whereas other AITD genes have had very low ORs of <1.5. Existing genetic models could not "explain the high frequency of AITD in the general population (up to 5%)," and so the authors suggested a model to combine the effects of genes and environment.
[PMID 27586448] See also this 2016 article titled "Recent Advances in Autoimmune Thyroid Diseases" for advances since 2010. In addition to discussing the genes involved, it noted that selenium and vitamin D were the main dietary elements.
[PMID 27296629] A 2016 article titled "Exacerbation of Autoimmune Thyroiditis by CTLA-4 Blockade: A Role for IFNγ-Induced Indoleamine 2, 3-Dioxygenase" claimed that the CTLA4 "blockade" worsened autoimmune thyroiditis, by various means. It cautioned that some cancer medications employ CTLA4 blockade as a strategy and may result in autoimmune thyroiditis in susceptible individuals.
See more at SNPedia page on Hypothyroidism