What is perhaps a more pressing question is what would happen to the Anglican-Methodist Covenant were either church to change its opposition to gay marriage. Would a sudden change by the Methodist Conference in 2019 or 2020 scupper the long proposed deal…?
It certainly might make the strong conservative base on the Church of England’s ruling general synod less enthusiastic.
But difference in teaching on sexuality is not officially a block on sharing ministry.
The Church of England is already in direct ‘communion’ with its sister Anglican churches in Scotland and the US. This means that priests in both churches are recognised as such by the Church of England and so they can, as long as the local bishop agrees, come and minister in CofE parishes.
Both the Episcopal Church in the US and the Scottish Episcopal Church permit same-sex marriage, and while they faced sanctions from the wider Anglican Communion, they remain in communion with the CofE.