This may seem old fashion to some folks, but I've always understood a priest to represent the bishop; I work for the bishop, not a congregation. To me, the smallest division in the Church is the diocese. As St. Ignatius said, "Where the Bishop is, there is the Church."
Consequently, I am a person "under authority." If the bishop tells me to do something, we might discuss it, but saying no is never an option. If I ever had to say no to my bishop, I would resign my position, and leave the diocese. I have no problem telling the parish leaders "No!" when necessary, however (not always with an exclamation mark, though...usually more like, "...what if we did it this way instead?").
There are at least two dioceses in the Episcopal Church in which I cannot serve because they do not accept the ordination of women. Out of respect for their theological position, I would never take a cure in these two bishops' jurisdictions. I am quite sure their position is in error. I find the type of theology from which such positions spring to be tedious and legalistic, let alone denying the gifts given to the Church through the ministry of women priests and bishops for the last two decades.
But it's not just about theology. If I was serving in one of these dioceses, and for some reason planned for a visiting woman priest to celebrate the Eucharist, there is a very good chance that I would receive a Godly admonition from the bishop to cease and desist. In that situation, most likely, I would disobey the bishop, and fully expect to be brought up on charges in an ecclesiastical court for my disobedience. Consequently, such placements are simply not an option.
I've never felt terribly oppressed by this. There are a few other bishops whose diocese I avoid as well, based more on leadership style, extreme conservatism and stories from other clergy. I've always considered researching the bishop and the diocese part of my homework before accepting a call.
When I hear stories about David Moyers and Sam Edwards deciding to take on their diocesan bishop, I have to ask; what in the world were they thinking? If they won't accept the authority of a bishop whose theology they disagree with, why in the world did they accept the call in the first place? It wasn't like Bp. Bennison or Bp. Dixon hid the fact that they were progressives.
Sadly, we seem to be following the rest of the Protestant traditions; slowly slipping into congregationalism.
UPDATE: Just so you don't think this is simply another eccentric (or heretical) idea that Jake dreamed up, I refer you to a piece from April, Where Have All the Catholics Gone? in which I quote an excellent address on this topic by Bishop Paul Marshall. Here is the most relevant segment;
There are two grave theological errors afoot today. They come from the very real anxiety that some feel about bishops who persecute members of the right; anxiety is not, however, a reliable basis for theology.
The first error is that a priest can declare her/himself to be out of communion with her/his bishop and still be a priest. The priest is there as a partner of the bishop's in a "ministry which is mine and yours in this place." To reject that relationship is to put oneself out of business as a priest, plain and simple. St. Jerome to the contrary notwithstanding, the presbyterate is not the foundational order of the ordained ministry. The Eastern Orthodox churches are so clear about this relational basis for a priest's function that nobody in the west can bear to discuss their position for very long without trembling.
The second error is the proposal that a bishop cannot choose who will be among the trusted colleagues, cannot determine what priests serve as the bishop's associates in parishes or other ministries. It is the bishop's trust that the letter of institution expresses. If a rector can be imposed as a colleague over the bishop's conscientious refusal, one wonders how the relationship can in fact function. Much more, one wonders what it means theologically. Even the Lutherans cannot imagine this, despite their curious position on ordination.
If we are to have historic order in any meaningful sense of the word, we are going to have to accept the fact that we may not always like episcopal or synodal decisions. For priests to obey their bishops only when they happen to agree with them is not obedience at all, and to this commonwealth's endemic congregationalism we unhappily see added presbyterianism of the most unsubtle kind these days. Again, by clearly teaching the simple doctrines of the catechism and by our living out our relationship with each other, we can overcome this misperception.