Generally speaking, those who have power and lead the community prefer unity. They do not want diversity of thoughts because they have to maintain the status quo and do not want to be challenged. But everyday people are not really concerned about such a status of unity. They need more respect, dignity, and equality in their lives. Often unity becomes the language of control. This is true to the case of the Roman Empire. Even if diversity is allowed in the Empire, it is limited to religion and culture. That is, people cannot protest the rule of Rome. They have to speak the language of Rome and its Empire. They are forced to stay in their place of identity. They are told again and again that society is one body with an emphasis on unity. In the name of unity, the unfortunate are taken for granted and suffering is taken for granted.
Even in the church, pastors talk about the unity of the church, based on 1 Cor 12:27 ("You are the body of Christ and individually parts of it"). In their preaching, members of the church are expected to think in the same way without asking questions about church doctrine or any teachings about God. But Paul does not mean that members of the community have to be in consensus in all matters; rather, his point to the Corinthians is they have to have the same mind of Christ. In other words, they must live like Christ, being ruled by his spirit, and imitating his faith.
In a traditional frame of interpretation, scholars read "the body of Christ" as a social body with an emphasis on unity (homonoia) just like Stoics who tell members of the society to be one without asking about injustices (c.f., the fable of Menenius).
But there is an alternative reading of this body metaphor "as a way of living" (as I wrote Christ's Body in Corinth about this). That is, Paul's point is: you are a Christic body. You are to be ruled by Christ, individually and communally. This way of reading of the Greek genitive is certainly plausible as we see in Rom 6:6: "the body of sin might be destroyed." Here, "the body of sin" is construed as "sinful body" or "sin-ruled body." In this reading of the body metaphor, Paul's emphasis in 1 Cor 12:12-27 is not unity but the lack of true diversity due to the lack of Christic embodiment. Some Corinthians claim that they are wise in Christ and saved already. Others boast about their gift of the spirit: speaking in tongues, prophesying, and even their knowledge. Given these problems of the disembodiment of Christ, what Paul asks them to follow is not the mere language of the oneness of the body just like a social body (metaphorical organism) but the radical identification of their living with Christ. For example, in 1 Cor 6:12-20, the Corinthians are advised not to sleep with prostitutes because they are parts (mele) of Christ. Here, we have an image of Christ's body (as a human, not as a social body) as opposed to prostitutes' bodies. Paul's conclusion in this passage is that they have to glorify God in their body--through their living of Christ in a most faithful manner as Christ lived for God.
*Note: Most recently, I wrote "Reimagining the Body of Christ in Paul's Letters." This book deals with the body of Christ extensively in view of Paul's gospel.