I have an anaphylaxsis allergy to milk, peanut, tree nuts and seafood. The popcorn freshly popped at the theatre has been safe each time we have sailed with Disney (Dream, Fantasy). Each cruise, I will wander by when they aren't busy (usually as they are opening/setting up when there is no line and they are kind of relaxed) and explain I have food allergies and ask if I can see the ingredient info -- they hand me the package. On our last cruise on the Fantasy in December 2017, it was the same as the stuff WDW uses for the parks.
"Buttery" flavour, but not actual butter, just like at most movie theatres
But, always check, to be safe.
SW