I am a member of the Church of Norway (CofN), and I am currently in seminar. I am also part of a group of priests called Carissimi, who seek alternative episcopal oversight. To flesh out the reasons for this, I will here post a slightly edited version of a comment I made on an online forum. I hope this clarifies the reasons for this.
When we talk about alternative episcopal oversight, we need to make a crucial distinction between doctrine and opinion. And to illustrate this, I will use two examples: the decision of the Church of England (CofE), in 1992, to allow women to be ordained to the priesthood and the decision of CofN, in 2006 (confirmed in 2007), to allow practicing homosexuals to be ordained to the priesthood. The reason I use these is that the first marked the demand for (and introduction of) alternative episcopal oversight in CofE, while the second marked the demand for (and hopefully the introduction of) alternative episcopal oversight in CofN.
There was a qualified difference between pre and post 1992 (in CofE) and pre and post 2006 (in CofN). Before 1992, there were bishops in CofE who believed that women could be ordained as priests. But what a bishop privately believes is not that interesting. A bishop is not appointed to pontificate privately. He is appointed to ensure ecclesial unity (both sacramentally and doctrinally), to teach and uphold the doctrine of his Church, and to ensure that proper doctrine be taught. Now pre 1992, CofE taught that women could not be priests. Therefore any bishop would be responsible to uphold this. Post 1992, however, we see something new: We do not (merely) see CofE changing position (saying that women could be priests), but we see that CofE said that it was ecclesially and canonically legitimate either to hold that women could not be priests or to hold that women could be priests. We saw something similar in CofN in 2006.
In 2006, the Doctrinal Commission of CofN issued a document on the question of homosexuality and Scripture. (The link is in Norwegian.) The Commission was divided in two on the question of the marrying of same sex couples and the ordination of practicing homosexuals. Prior to 2006, CofN had one official view, even if there were many bishops who held other views. After 2006, however, there have been two official (and contradictory) views on this question, which means that it is now ecclesially and canonically legitimate either to hold that same sex couples cannot marry in the church and that practicing homosexuals cannot be ordained, or to hold that same sex couples can marry in the church and that practicing homosexuals can be ordained. Because of this, a group of priests and lay people have sought alternative episcopal oversight.
The point of alternative episcopal oversight is that there is a new situation, ecclesially and canonically. The important thing here is that the unity of the Church is both doctrinal and sacramental. This means that if there is a real internal (ecclesial and canonical) schism (i.e. that two opposing views are both legitimate), then this needs to be expressed episcopally. The question is not: What do we do about these [insert adjective] bishops? Thus it is not a question of ‘putting up with’ certain bishops. I don’t particularly care what my bishop privately holds. The question is rather this: What do we do when we have two contradictory views which are both legitimately (ecclesially and canonically) taught within the same Church?