I think your understanding of the Anglican church is flawed. You absolutely do have to sign on to specific doctrines. Every baptised member of the Anglican church must assent to their baptismal oath prior to receiving the sacrament. There is room for diversity of course but not in away that goes into the realm of heresy and denial of the articles of faith.
You see, the problem for the cultural relativist is that to make his/her views acceptable, first the Bible must be denigrated, and then it must be denied that anything specific teaching or doctrine must be believed in order to be a member of any certain church, or even to call oneself a Christian. Thus, we have people like Spong who denies the central doctrine of the bodily resurrection, the one doctrine which differentiates Christianity from every other religion, and yet he can call himself a Christian and even be a bishop in a "Christian" church.
When deriving anything about Adam and Eve, what matters is not our placement or treatment of them, since their biblical themes are more than just lore, but the overall tapestry which happens to involve them and what is being conveyed. In the Bible, dates and events are very important, yes, but it's the names which gives us the truth in all senses of the word. Since they are integral to the message communicated to us, Adam and Eve are literal (real). Their lives and what's going on around them is best understood when reading the Bible in its theological essence. One thing we have to remember about the biblical text is that when it comes to interpreting its contents that both methods, lexiconal (expression, speech) and conceptual (application of principles), are always considered. Their story is a story in which God singles them out for personal love and responsibilty. The end goal is that whatever they do and set their minds to, they come to accept God by trusting Him in grateful grattitude. This is only possible, due to their disobedience, through learning to know God. What He stands for is what they are to stand for.