What is the established church's (Church of England's) view on the theology of the eating of the fruit of the tree of knowledge of good and evil as being a metaphor for the act of questioning God's judgement and requirement for acquiescent obedience?
The Church of England doesn't generally have a published doctrinal stance on this sort of thing.
However, there is a passage in the Catechism which might be relevant.
Eve, and Adam, certainly didn't follow that: by disobeying, they did not put their whole trust in God. Whether that turns the story of the apple into a metaphor can only be determined by the individual — the Church of England holds that it's reasonable to believe that the first few chapters of Genesis are literally true and it's reasonable to believe they are allegory or metaphor.
Acquiescent obedience would imply simply being an automaton. No-one is an automaton; God gave Man free-will, and he's used it. It was the basis for the Fall in the first place.
The Catechism continues:
This certainly sounds like "acquiescent obedience", but bear in mind that this was written in the seventeenth century for young people coming to confirmation (and it had to be learned by heart!). These two questions follow directly after the recitation of the Ten Commandments and their distillation into the two Dominical commandments, Love God and Love thy Neighbour.
God's will for mankind is to love God and love one's fellow-man. The Catechism makes it clear that there is no greater calling, since it is God's; is that "acquiescent obedience"?