No, we certainly don't inherit diseases from our parents. But the susceptibility of developing an autoimmune disease is passed down from parent to child. Now whether a person actually develops the disease largely depends on environmental factors. For example, if my memory serves me correctly I believe that among identical twins there is a 40% chance of the both twins having Psoriasis if one twin develops it. If the development of Psoriasis was purely based on genetics there would be a 100% chance, not a 40% chance. With fraternal twins the chances are much less, maybe a 5% chance. And among the general population on 2% has the disease. At any rate, I would expect Hashimoto's follows a similar pattern.