More ligaments in the Acts book...
Acts 15 gives us an inspired picture of how conflict would ideally take place. Because we are fallen creatures subject to sin, God lets us make things much more complicated than it would need to be. But Acts gives us a picture of how conflict might be resolved.
First, conflict is not bad in itself. There are no doubt some Christians who think that all conflict points to a spiritual problem of some sort. This is not the case. Sometimes good causes compete for the same resources. Sometimes two individuals both are asserting appropriate values that need to be prioritized. Sometimes in our limited understanding, we have to struggle together to find the truth.
People, values, and trajectories inevitably come into conflict and, at that point, Christians have to wrestle together to find the best way forward. There are at least three phases to the resolution of conflict in Acts 15. First, after the conflict comes to a head, everyone comes together, and everyone is heard.
It is of course possible to head conflict off at the pass—that would perhaps be ideal in many instances. And as hard as it is to say it, there probably is a time not to bring everyone to the table, especially if some of those involved are completely inflexible. But in a perfect world, everyone would come together and get a chance to share their perspective on the facts of the conflict and what they think is the best way forward.
The second phase is when the proper authority makes a decision. Of course, people do not always agree on who the appropriate authority or decision-making body is. One of the benefits of organized churches and denominations is that they often have laid out clear lines of authority so people can know when a matter is officially settled. These channels of authority are best laid out in “peace time,” so that they are already agreed in the moment of conflict itself.
Finally, there was a phase of submission. Historically, of course, we have reason to think that the disagreements of Acts 15 continued. Sometimes conflict merely goes underground, and the war becomes guerrilla warfare, with back-stabbing and all. But Acts 15 gives us the inspired, ideal picture, where all the parties involved submit to the decision made by James and the elders, the proper authorities.