I was hoping someone else would answer this, because I too am curious what they mean when they say people with autoimmune diseases may be more at risk for serious complications. I am not a medical professional in any way, so please know that below are just my thoughts on this. (And I googled this looking for an answer as well, but couldn't find anything definitive at the time)
I am assuming when they say people with autoimmune diseases, they are referring, to people who are on immunosuppresive drugs to treat their diseases, since many of these drugs with suppress the entire immune system to some degree, slowing down or preventing an immune response. There are so many different autoimmune dieases, and some might make the coronavirus worse, including ones that cause damage to the lungs or respiratory tract, ones that cause underlying health conditions like diabetes, ones that affect the whole body like lupus.
If you are taking medication for Hashimoto's, it is usually synthetic or natural thyroid hormone, which is not an immunosuppressive drug, just something that is restoring your thyroid hormone to "normal" levels, so should not impact your immune response.
I have noticed with my Hashimoto's, I've had many more seasonal allergies than the average person (e.g. my family members who also have seasonal allergies but no thyroid issues), but since my seasonal allergies started around 2006 when I was 25 years old, I've had a lot fewer colds and flus than I did when I was younger.
I "think" my immune system, especially my respiratory tract immune response is tuned way up, but this could just be because I'm a woman, and women tend to have stronger immune responses than men, and we now have a flu vaccine which lowers my risk of getting the flu, I'm not in school getting exposed to viruses as often, etc.
But, all people are different, and just because one part of the immune response (Bcells producing antibodies against the thyroid) is overactive does not mean the entire immune system is overactive, and people with Hashimoto's should still take the same precautions as everyone else. Wash hands, minimize contact with other humans, social distancing, etc.
I live in Ohio, and I am currently trying to avoid all trips outside the house except for groceries and pharmacy (and running), because I want to minimize my chances of getting the virus as well as preventing spread if I have been exposed, to minimize the burden on the health care system.
I do still go on a run (by myself, just like every other day since my last race in October 2019) almost every morning, because that helps keep my energy levels higher throughout the day (I'm assuming this has something to do with hypothyroidism, and on days I do not run I feel so much more fatigued) and it is good for my mental well being and mood control, and brings some normalcy to this whole thing for me.
I hope you are doing well and hope you stay safe and healthy.
From what I know about this, Sarahjogs is right that Hashimoto's wouldn't make us a whole lot more susceptible to the coronavirus than many others, but of course, as noted, we're all different, so what might be true for me wouldn't be for someone else.
When they talk about immunosuppressed people, they mean those whose immune system are really weak. One example would be a sister of mine who is remission from lymphoma and leukemia. The chemo she required to accomplish her remission destroyed her immune system and she now requires immunotherapy to live. If she were to catch this virus, she would not survive. People with heart, lung problems (such as another sister with lung cancer) and those with diabetes (my son) are typically the main ones who are susceptible but of course, others, such as my daughter with Lupus would be very susceptible because Lupus attacks the entire body, which weakens the whole immune system, whereas Hashimoto's is confined to attacking the thyroid.
If one of us with Hashimoto's (or myself with Pernicious Anemia also, which gives me 2 autoimmunes) called our doctors and asked for the test for coronavirus due to our autoimmune conditions, they would, most likely tell us we can't get in line yet unless we meet the criteria for having the virus.
There are other autoimmune conditions that would weaken one more than some others, but the antibodies that cause autoimmune conditions, such as Hashimoto's and other diseases that attack our own bodies are not the same as how our bodies attack viruses and bacterial infections that we get.
When we get a cold/flu or possibly this virus, our white blood cells ramp up and try to knock it out because we don't have antibodies against something we've never had before or been vaccinated for. It's my understanding that we will produce antibodies against this virus once we've had it, so we would, in effect produce an immunity against it, but that's not something they're 100% sure about. Some of the doctors are saying our immunity might be short term or long term... they just don't know that yet.
It's all pretty complicated and I've totally simplified it, but I hope this helps a little bit.
The main thing is, as has already been noted - wash your hands often, disinfect the surfaces you touch often, maintain your social distancing and practice all the precautions you can to protect yourself. Last, but not least, listen to what the authorities are telling us to do so we can slow down the spread of this thing.