First, it is a practice contrary to the scriptures as they have been consistently interpreted by the two thousand year tradition of the churches of both East and West.
Second, we hold that the use of GM crops by individual provinces of the Anglican Communion, without inter-provincial agreement or consensus, is a schismatic act, impairing communion between provinces by subverting the interchangeability and mutual recognition of orders between them.
Third, mindful of the unity for which Our Lord prayed on the night before he died, we are bound to repudiate an action which has willfully placed a new and serious obstacle in the way of reconciliation and full visible unity between Anglicans and the Roman Catholic and Orthodox churches.
So ultimately, the campaign is saying "we have no reasons, but tradition must be upheld!" Strong point of argument, people.