Were (the Church of England's) pastors priests of the Catholic Church (as the Prayer Book insisted) or ministers of a Calvinistic sect?
Pretty much the central question to be answered for the purposes of settling the issue of Anglican identity, is it not? My answer is that is that our pastors are in fact priests of the Catholic Church, not ministers of a Calvinistic sect, BUT that Anglicanism at least makes room for certain doctrines that came to be associated with Calvinism. Said doctrines are not necessarily "Calvinistic", however, as they antedated him, in certain cases by a thousand years.
We are not Presbyterians with prayer books, however, and the English Reformation didn't end with the Settlement. Hooker and the Caroline divines are as important to classical Anglicanism as are Cranmer and Jewell, and what's more, I don't believe we can ignore the Tractarian legacy in our attempt to articulate Anglican identity.