Thanks very much for confirming my suspicion @Scott Adams! That helps a lot because I'm really trying to track down and get rid of these sources of cross-contact and so I'm going to just rule out the draft ciders and hope that helps. Also @Rogol72 its nice to hear you haven't had a problem on that side of the pond - draft cider lines being used for cider only certainly sounds like the right way to do it, but I think that must not always be practiced over here!
I didn't ask a doctor about this actually. I did ask several doctors a long time ago and they told me gluten has nothing to do with hashimoto's. One of them told me to do a gluten challenge to test for celiac, but at the time I was in graduate school so couldn't afford to be even more ill than I was.
If you have the symptoms, I really don't advise you to do a gluten challenge. It messed me up mentally and physically for months. At the same time, I benefitted from doing the challenge in the sense that it convinced me that all my symptoms were truly from gluten - even stuff like insomnia! So now I am terrified to eat gluten, whereas before I would have a little once in a while and not notice anything dramatic.
I am in a similar situation where I can't feasibly do a gluten challenge but have all the symptoms and I have 2 celiac genes. I'm curious if your doctor advised you to eat as if you had a diagnosis or if they were more dismissive about it.