Well, while the website definitely puts a lot of distance on allergen-free; if you can't offer a food allergen-free then you shouldn't. Same as if you can't take the bones out of a chicken wing; don't offer boneless wings.
However, if you go to the restaurant in-person and you ask the server who asks the chef and they both say it can be done allergen-free on multiple requests I think it's safe to safe that the website's disclaimer is overriden. Which is what the lawsuit claims [1] (I wish I could get a courtlistener link but I had no success [2]).
[1]: https://www.scribd.com/document/708687171/Raglan-Road-Lawsui...
[2]: https://www.courtlistener.com/?q=Disney&type=o&order_by=scor...