I won't comment on ASA's policy per se
. I believe that all are welcome to contribute to this site.
What I would say is that the doctrine of the Trinity is part of mainstream, orthodox Christian belief, whether in its Roman Catholic, Eastern Orthodox, or Protestant forms (save Enlightenment Liberal Protestant theologies, many of which arguable are not actually Christian).
You say above that the Nicene Creed identifies only Father and Son as being of the same substance; this may be technically true, but the Creed also says that the Spirit is the Lord and Giver of life and is to be worshiped together with the Father and the Son. But even without that, its affirmation of the Father and Son already rules out unitarianism.
I don't say this to exclude. I think the ASA is about dialogue, though as a Christian organization it regards trinitarian belief as basic to Christian faith and confession.
Consider the following quotes (the books cited may be helpful to read):
“The doctrine of the Trinity can be regarded as the outcome of a process of sustained and critical reflection on the pattern of divine activity revealed in Scripture, and continued in Christian experience . . . Scripture bears witness to a God who demands to be understood in a Trinitarian manner.” (Alister McGrath, Christian Theology; Wiley-Blackwell, p. 239).
“For the Christian confession, the doctrine of the Trinity makes all the difference in the world, for that doctrine is at the heart of the Christian gospel, and so at the heart of the Christian understanding of the nature of God and of the manner of God’s relation to the world” (John Webster, Holiness, Eerdmans, p. 36).
“The doctrines of the Trinity and of the incarnation thus form together the nucleus at the heart of the Christian conception of God and constitute the ontological and epistemological basis for the formulation of every Christian doctrine.” (T. F. Torrance, The Christian Doctrine of God, T&T Clark, p. 30).
These are representative of the broad consensus of the Christian tradition. For a recent biblical approach, you might want to check out Koestenberger and Swain's book here: http://books.google.ca/books?id=v6uJQy1lB_gC&printsec=frontcover#v=onepage&q&f=false
My suggestion is to do some more reading on the Trinity to see why it's so central to Christian belief. And then continue the conversation.
I don't want to comment on the membership policy; that's for others to decide. But I would suggest that the statement of faith cannot be modified as you suggest without purging it of its distinctively Christian content.