I can only tell you our experience with the BOG cupcakes...
We have always spoken with a chef for TS and either a manager or looked at the allergy book for CS. So we were a little skeptical when ordering with the kiosk with allergies. (Lunch) The CM helping us order assured us every choice unsafe woud be eliminated off the kiosk choices. Which there were several of, and several modifications came up, such as different bread, etc. (for peanut and tree nut allergies). (For example, DD wanted the vegetable quiche, but that choice was eliminated for her so there must be something in it that is not ok, my guess is the crust...)
They must get this a lot, because we kept looking at him, like are you sure?? and he kept saying, really, it's all ok if the choices still remain. So we went with that, as we have trusted Disney for years with DD's allergies.
Her food was brought out by a manager and had an allergy stick in each item she ordered, it was not brought out on the cart with the other food.
Still, she stared, unsure, at the two cupcakes we were going to share to taste each one, and she couldn't believe it, as almost all baked goods Disney has are off limits to her.
She is severely allergic to both peanuts and tree nuts, and we don't even take a chance with foods that are peanut/tree nut free but are manufactured in the same facility.
Really, my heart raced as she started tasting them, and really wondered if taking the chance was even worth it. I had my eye on my purse for her epipen and benadryl even, lol. She was fine and the delight to see her eating them was so much fun! (We had the chocolate and strawberry.) I tasted each one and let her eat the rest...of both, lol. Shhh, don't tell her I told you that.
A rare occasion and a special treat.
That was our experience and as always, I would suggest each party follow up on your own to be sure.
I hope everyone else gets to enjoy the BOG offerings safely! Have fun!