Physician-scientist here. My graduate work was in an immunology lab. Just wanted to clear up some confusion I've seen in multiple posts.
While both peanut allergy and celiac disease involve pathogenic immune responses, they represent very different types of problems and this study's results do not suggest any relevance to celiac.
The peanut allergies that they are referring to in this study are one of the most striking examples of what's known as a Type I hypersensitivity (IgE-mediated/anaphylaxis). In this type of reaction, high levels of IgE, a class of antibody, generated toward a specific antigen become loaded onto mast cells and on re-exposure, cause mast cell degranulation and subsequent smooth muscle contraction. For this reason, anaphylactic responses frequently involve closing of the airway, nausea/vomiting, and other dysregulations of smooth muscle activation and require a strong adrenurgic agonist like epinephrine to counteract this activation.
Celiac pathogenesis is not a Type I hypersensitivity. To my knowledge, the exact mechanism of pathogenesis is not known, but it is likely a combination of Type III (antibody-mediated) and Type IV (T-cell mediated) hypersenitivities.
Anyway, I'm not trying to ruin anyone's hope here, but this study has no relevance for celiac. What this has shown is that there is the potential for food allergies to be systematically eliminated with long-term increasing exposure to the problematic antigen, in this case, peanut antigen. This has been done for some time with other, less aggressive types of IgE-mediated conditions like dog and cat dander allergies. So in that way, it's not all that surprising of a result, but I'm certainly glad to see that this was able to be done safely. This is really great news for the millions of people out there with anaphylactic food allergies.
All that being said, I do hope that celiac can be managed more effectively with immune-modulatory (or other) treatments in the future and my sympathies go out to those who have been affected by this horrible disease.