Reporting back with info from out recent trip - 8/7 - 8/18. My son has celiac disease. He had one minor issue on the last day of the trip. He's not sure what it was from but thinks it may not have been any food he ordered, but rather from drinking out of the wrong water bottle.
We used mobile order for counter service with no problems at
AOA resort multiple times
Polite Pig
Peco's bills - chicken nachos
Liberty Tree Market turkey leg (maybe not mobile order)
Columbia Harbor House
Aloha Isle dole whips
Flame Tree
Regal Eagle
Pizza Rizzo
ABC Commissary
In person order
Australia Food booth, Donut Food booth (Strawberry Smoothie)
Restaurants - Liberty Tree Tavern, Yak & Yeti, Hollywood & Vine, Oga's Cantina (drinks), Nomad's Lounge (churros), Coral Reef, Crystal Palace
We also ate at the following places at Universal: Margaritaville, Mythos, Confisco Grill, Hard Rock, The Kitchen, NBC Grill -- we avoided counter service. He did have frozen Butter Beer as well