The first thing to note is that it is not only difficult, but impossible, to argue that what the bishops are proposing is not a departure from teaching contained in the bishops’ statements concerning Civil Partnerships and same-sex marriages in 2005, 2014 and 2019. In these statements the bishops said that public prayers should not be said for same-sex couples. What is now being proposed is that such prayers should be offered. If the Bishops previous teaching constitutes doctrine for the purposes of clause (g) of the February General Synod motion and for the purposes of the Canons, then what is proposed is contrary to the doctrine of the Church of England.
The bishops argument seems to be that this change from previous teaching is not indicative of a change in any ‘essential matter’ because they are not proposing any change to the Church’s doctrine of marriage or its doctrine of sexual ethics which says that sexual intercourse should only take place within marriage (meaning a marriage with two people of the opposite sex). Where their argument falls down is that if the Church of England’s doctrines of marriage and sexual ethics are viwed alongside the Church’s doctrine concerning the need for repentance and forgiveness for sin, then what they are proposing is necessarily a change of doctrine in an ‘essential matter.’
To understand why this is the case, the point that has to be grasped is that it is an absolutely essential part of Church of England doctrine that in order for people to be rightly related to God in this life and eternally happy with him in the next, they have to acknowledge, repent of, and confess their sins, not only in private but in the context of public worship, so that their sins may be forgiven and no longer constitute a barrier between them and God.
This doctrine is made crystal clear, for example, in the opening paragraphs of the service of Morning Prayer in the Book of Common Prayer:
Read it all.