I've done about 7-ish (?) gluten free Disney trips by now since having to go gf...
Raglan Road has gluten free fish and chips, but I get the gf fish and onion rings!! My gluten eating family steals them every time I get them, they are that good. Cookes of Dublin, the quick service for Raglan Road, also serves gf fish, chips and onion rings.
I have never had an issue with ordering gluten free. Disney is wonderful with allergies in general. I've had chefs make me special meals based on what I liked, and I've ordered from quick service places with no issue whatsoever. You'll be fine! I feel safer eating in Disney than anywhere.
Satuli bowls are great, Flame Tree BBQ, Sunshine Seasons, Be our Guest, all of them QS and have interesting gluten free items. Other QS places like Cosmic Rays, ABC commissary, Casey Jr. etc have hot dogs and burgers with gluten free buns.
And...since you'll be there in May (as we will be too!) Flower and Garden festival in Epcot will have gluten free items in some of the booths. Keep an eye out for the menus in the next month, they will have the gf items clearly marked for each booth, if offered. Food and Wine festival also has gluten free items and is our other time of year to visit.
If you decide to splurge for table service; Raglan Road, Biergarten, Ohana, Spice Road Table, Sanaa, Bongos and Tusker House are some of my favorites. I've had breakfast also at Ohana and Tusker House (cheaper $) with gf waffles, which was a treat. I've also had the beignets at POFQ, which were a nice treat.