I dunno, maybe I'm weird or something, but I don't hesitate to tell anyone why I can't eat their food. I'll say, "No thanks, unfortunately that type of food will make me sick." Of course it leads into other questions, but I'm not embarrassed or ashamed (I'm not suggesting that the OP or any of us are) and frankly I take every opportunity to educate someone on Celiac. If my two minute conversation could potentially help someone recognize their own symptoms (or the symptoms of a loved one) and get them help, then its all worth it for me. This is a very misunderstood disease and diet and I feel satisfied when I can correct information. Its all about confidence. If you explain Celiac with confidence, my experience has been that people listen better and accept what you're saying - the conversation also doesn't turn into a pity session or "oh my god I feel so bad for you." Yes I have Celiac, no, I cannot eat your food, and we can move on with the conversation....it also prevents the same food offerings at future events with these people.
All that being said, I'm not suggesting that everyone should go out with their "I'm a Celiac" t-shirt on and start preaching on street corners. It's all about your comfort level and if you even feel like explaining it that day (there are some days where I'm either tired or annoyed and I just decline food without saying anything else). I just wanted to share because I've never had a negative reaction for sharing why I couldn't eat someone's food - in fact it only led to more understanding on their part.