I haven't stayed at any of the All Star resorts, but I have stayed at a few different resorts around WDW. One thing that's been consistent is that the chefs really go out of their way to accomodate food allergies. Because my kids have difficult lists of allergies to work with and we usually eat one meal per day at the resort, I typically request to speak with a chef at the resort. The chef tells me what kinds of safe foods they have on hand and ask about my kids' favourite foods so they can make sure to increase inventory of those foods during our stay. I just spoke with a chef at POFQ yesterday and he's even going to play around with some recipes to see just what kinds of baked goods he can come up with for my one daughter who can't even eat the French Meadow brownies and cookies (they're gluten and dairy free but they have eggs which she can't eat; none of the standard prepackaged baked goods are safe for her). He was telling me some of the things he's going to try to figure out and I was telling him it was totally not necessary (like making a gluten, dairy, egg and yeast free Muffaletta - WOW) but he insisted that he wants to at least try. The chefs at the other resorts were also just as amazing. In February, DD11 chose to eat gluten and dairy free mac & cheese and chicken strips almost every day as well as safe Mickey waffles for breakfast since these are things she does not get often at home. The chef at POFQ said he can easily do the same.
You'll have such a great experience that you'll never want to vacation anywhere other than WDW ever again.