To be fair, cue was most likely originally a misspelling of queue. The meaning is just too similar to be a coincidence.
To be fair the standardization of Written English did not take off until the 1800's. And many of our words come from other languages which may or may not have had several spelling variations of its own word. In this case: Cue, Coe, and Queue are from old French. Que is from Spanish and is a homophone to others so it ends up getting mixed up in spelling a lot. Of course Cue in English has a different meaning then the Old French word. We can thank the various dictionaries produced in the 1800's for that; nearly every publishing house made their own for sale; finally with Webster in the United States and Oxfords in England winning out as being the "Standards" for spelling.
The English language is very much a bastardization of everyone else's. :)
It is not the only language that has had issues with drifts in spelling and the spoken language itself; needing a dictated standardization to try and stem the drifts. Mandarin is another example that has had issues due to the vastness of the Chinese empire, its limited transportation network and relatively isolated communities.