Cue vs Queue
Both of these words are pronounced the same, but they have very different meanings and are not interchangeable in the slightest.
Cue has one meaning:
A prompt or signal for something like an entrance or a response.
Example:
"That's my cue! I gotta go."
Queue also has one meaning:
A line of people.
THAT'S IT.
Example:
"We should go queue up if we want good seats."
One can't be switched out for the other. You can't drop the last "ue" off of "queue" to make "que" because that has no meaning at all in English.
I understand Britishisms slipping in because people from all over write fic, but really, queue kind of rips the reader from the story. It's not a term that's commonly used in the US. If you want to use queue, go for it, but I strongly recommend using something else like "wait in line."
But please, do not use queue for cue.