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.
What is thy duty towards God?
My duty towards God is to believe in him, to fear him, and to love him, with all my heart, with all my mind, with all my soul, and with all my strength; to worship him, to give him thanks, to put my whole trust in him, to call upon him, to honour his holy Name and his Word, and to serve him truly all the days of my life.
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:
What is thy duty towards thy Neighbour?
My duty towards my Neighbour is to love him as myself, and to do to all men as I would they should do unto me: To love, honour, and succour my father and mother: To honour and obey the Queen, and all that are put in authority under her: To submit myself to all my governors, teachers, spiritual pastors and masters: To order myself lowly and reverently to all my betters: To hurt nobody by word nor deed: To be true and just in all my dealing: To bear no malice nor hatred in my heart: To keep my hands from picking and stealing, and my tongue from evil-speaking, lying, and slandering: To keep my body in temperance, soberness, and chastity: Not to covet nor desire other men's goods; but to learn and labour truly to get mine own living, and to do my duty in that state of life, unto which it shall please God to call me.
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"?