Just returned and can report on this, gluten and nuts especially. I didn't run into nuts anywhere, and if there are nuts in something it's very clearly marked. The options are far less than normal, I won't lie. BUT they're just as good about safety.
MK: Skipper Canteen was great as always. GF Tastes Like Chicken, Pao de Quejo, and falafel. Got GF fries at Cosmic Ray's. For that, I had to ask to go inside to place an order. Allergy options are on mobile order, but fries aren't, and they gave me a bit of a hard time when I asked to go in...but it ended up fine.
EPCOT: We struggled here more than normal. The whole menu at La Hacienda can be made GF for the most part and they were great about allergies. We LOVE Tutto Gusto for their GF pasta but it's closed, along with Tutto Italia. Rose & Crown isn't operating a dedicated fryer right now (or, they weren't this past Thursday). F&W options were fine. For GF, the citrus chicken, pao de quejo, and pork belly were all good. The jerk chicken was fine, but A LOT of food, so worth the money. You can still do QS tacos at Mexico, and the chicken ones are GF. Chips there are GF too.
Hollywood: We didn't bother. We took the Skyliner over to RR instead. I know Backlot has a couple options but it's the ordinary chicken nuggets, etc.
AK: We didn't go this trip. I know they still have the GF churros at Nomad, and most of the options at Satuuli. They took our fav (pulled pork cheese fries) off the menu at Flame Tree which was disappointing. Pro-tip, they can make those GF if you ask.
Beaches and Cream: Pretty much the same options as pre-COVID.
Primo Pratto: SO GOOD. Go here instead of eating at HS. Delicious GF chicken sandwich with seasoned fries. Way cheap too.
Ale & Compass Market: we were still able to get GF Mickey waffles but it took a long time (they have to make them over in the actual Ale and Compass kitchen and bring them over). CMs were so kind about it though, and I had no issues.