Which is more important, correct doctrine or unity?
You can’t say both because these are at odds with each other. Doctrine is divisive. Nearly 2000 years after Christ, people have yet to agree on a single overall theology or doctrine. There are probably more different doctrinal beliefs in existence now than in the past. (Interestingly there are also an ever increasing number of denominations…)
There is much emphasis placed on unity in the New Testament. Jesus prays, “May [all who believe in me] be brought to complete unity to let the world know that you sent me and have loved them even as you have loved me” (John 17:23). Paul often talks about us being “one body” (Romans 12:4-5, 1 Cor. 10:16-17, 12:12-13, Ephesians 4:25, Colossians 3:15). Paul also specifically instructs us to “make every effort to keep the unity of the Spirit through the bond of peace” (Ephesians 4:3). Peter likewise says, “live in harmony with one another” (1 Peter 3:8). Paul thinks disunity is such a big problem that he is already addressing it by the tenth verse of 1 Corinthians. Other verses on unity include Romans 15:5-6, Galatians 3:28 and Philippians 1:27, 2:2. In addition to specific teachings on unity, a significant part of the New Testament is about interacting with other people, and most of the actions will bring people together as opposed to separating them.