Unanimity is a word that can be difficult to say. However, it's even harder to do. A simple definition of unanimity is: "agreement by all people involved." Here's an example of unanimity or uniformity:
Find a group of passive people who don't think very much. Then stand up in front of them and boldly declare something half-way reasonable, ask all who agree with you for a sudden show of hands (allowing them no time to ponder the concept). Most people will quickly raise a hand. If you are patient, people will begin to look around to see who hasn't raised a hand. Usually those holding back will soon become self-conscience and will gradually raise their hand.
Unity is much different. It's not based on agreement, but on love and commitment. Strong families usually have little unanimity, but lots of unity.
Historically, Christians have tried to build churches around unanimity by finding others who agree completely with their doctrine and church practices. The main problem with that approach is that it tends to alienate all the other Christians around the world who don't agree with them 100%.
Building on unanimity causes much insincerity, because if anyone openly differs with the party line, they are seen as a disrupter of the group. Thus, many believers in unanimity based churches, just go along with the crowd and (at least outwardly) agree with and conform to the group's dogma and procedures. They've been trained not to think or seek the Lord for themselves.
Unity is so much easier and more effective. It is built on a foundation of love. Unity understands that if someone doesn't actually believe something deep inside her heart, it does no good to force her to act like she does. Unity trusts that the living Holy Spirit will lead individuals to the truth. It also recognizes that we all "know in part" and are seeking God's truth together; so we don't have to agree on things that aren't foundational to Christianity.
Jesus' prayer for unity in the body of Christ (in John 17) will never be answered by an outward uniformity of doctrine or organization. Unity in Jesus has to be heart-to-heart. It will never work head-to-head! Unity lets people seek God themselves (and loves them while they do), without imposing the group's approach to God on them.
For a handbook about how to break out of the religious idea that unanimity is necessary, and experience the wonderful freedom of Christian unity; google the book: One Ekklesia: The Vision and Practice of God's Eternal Purpose.
