If you can, I'd be interested in the places you guys ate safely. I'm getting nervous about our upcoming trip. We're likely looking at counter service places, I'm worried since things aren't labeled, I'll get up to the counter with my crew and not know what to get myself.
Seriously, you'll be OK. Disney trains its CMs and the kitchen mgmt & chefs are very knowledgeable. What I usually do is take a look at the menu while I'm in line and pick 2 - 3 things that look 'good'. Obvs avoid breaded/fried items and things that as a rule have gluten (i.e. meatloaf, gravies). I usually pick one sandwich, a salad, and a relatively 'plain' meat entree. Inevitably one of them can be done GF. When the chef comes to talk to you, some of them will just ask 'Do you know what you might want?'. Tell them what you'd 'like' and if it can't be done GF, they'll tell you what can.
I'm a really, really picky eater (besides being GF), and there have only been two places I've ended up leaving without eating. One just didn't have anything that appealed to me, the other told me (incorrectly, it turns out) that they could not accommodate me.
As far as places I've eaten (this isn't a complete list, just off the top of my head);
DL
Carnation Cafe
Hungry Bear
BTMBBQ
Rancho Zocalo
River Belle Terrace (but it was pretty bad. Safe, but bad)
Blue Bayou
There's a cafeteria-style place in NOS, can't think of the name of it
Jolly Holiday
DCA
Flo's
Wine Country Trattoria
Smokejumpers
Pizza place over by Paradise Pier
Lucky Fortune Cookery (teriyaki bowl to die for!)
Mexican place over by Lucky Fortune Cookery
HOTELS
Storytellers
Steakhouse 55
Whitewater Snacks
You know, you can look at most menus on line. If you see something that sounds particularly good, post it here. I'm sure someone can tell you if it's OK or not.