Enough of the caveats.
It seems to me that just about everyone who discusses biblical teaching on ecclesiastical cooperation and separation recognizes several unavoidable factors that affect how much we are able to cooperate in gospel ministry with other professing believers, how much we are compelled to withdraw from such fellowship, and when we are required to expose and rebuke error. I believe these factors include at least three specific dimensions:
1. Proximity to the gospelProximity to the gospel means that some doctrines are so essential to the nature of the Christian gospel that to deny the doctrine is to deny the gospel itself. The nature of the cooperation in view recognizes that different levels of fellowship and joint gospel ministry impose different demands on agreement. To serve as an elder-pastor in a church, I would need to have a very high level of agreement on most (but not all) issues with the other elders. My level of agreement with non-elder members of the church would be less. We could permit a person to speak in our church who might not qualify for membership. We might even be able to support other churches or ministries in some specific venture whose leaders we would not permit to speak in our church. Finally, exegetical certainty means that we do not possess equal certainty on all biblical doctrines. "Baptism for the dead" is not as clear as "Jesus is Lord." A more relevant example might be some matter of soteriology that could be very close to the center of the gospel, yet be less clear in the understanding of some than of others.
2. Nature of the cooperation in view
3. Exegetical certainty
To me, at least, it seems that denying the need to evaluate differences in light of these three factors will lead to complete separation of all professing believers from every other professing believer. In other words, demanding unanimity on any of these points precludes all Christian fellowship and cooperation with everyone who does not believe and behave precisely as you do, which I am pretty sure is everyone. If all doctrines are equally necessary, all forms of cooperation are equivalent, and exegetical certainty is irrelevant, then we must withdraw from everyone who does not agree with us on every possible issue in every possible pursuit.
I really need a graphic for this, but try to imagine a cube, obviously possessing width, height, and depth. Consider point #1 above to be width, #2 to be height, and #3 to be depth. Scenario 1: If a doctrine is essential to the gospel, the level of cooperation is quite high, and the exegetical certainty is likewise high, you have an issue that falls in a remote corner of the cube. Scenario 2: When a doctrinal difference has little to do with the gospel, the level of fellowship is minimal, and the biblical support for the doctrine is unclear, this issue falls in the opposite corner from Scenario 1.
A necessary corollary to this approach is some measure of independency. By that I do not mean that individuals or churches are islands unto themselves with no accountability to any other part of the body of Christ. I do mean that no individual or church is likely to possess precisely identical understandings of how to evaluate every issue of orthodoxy and orthopraxy and where it falls in the three-dimensional grid. These diverse understandings should be subject to discipleship and edification within and among local churches. On the other hand, the forces of shrewd maneuvering should not be used to foster control or to cultivate lording leadership of one local church (or para-church institution) over another local church. Similarly, a local church certainly should not abdicate its own autonomy in favor of blindless sycophancy to a church, institution, or movement.
I'm chewing on a potential fourth dimension. For lack of a better term, I'm calling it "the spirit of the age." This means that a doctrine might rise in importance because of its prominence in a contemporary groundswell against sound doctrine. An current example might be egalitarianism, the belief that both genders should share equally leadership roles in the local church and the family.
Some excellent and relevant discussions: