I promise you that I'm 100% for unity in the body of Christ.
I don't think unity at all costs is what Paul means when he says to work diligently to preserve the unity of the Spirit in the bond of peace. Unifying around Unity is not really unity at all, it's relational apathy.
Let me give two examples.
First, two women are in a church and having a discussion. One states that God is sovereign and in control and effusively glorious (okay, she probably didn't use those exact words, but you get the idea). The other states that she doesn't really worry about theology - she's just glad that God needs her. Unifying around Unity wouldn't sneeze at that, not even blink. Each has their individual experiences of God and off we go down the yellow-brick road.
But there's not true unity there. Because for either to cede theological ground to the other would be to invalidate their own stance. Choosing not to talk about it can be relationally harmonious (as with some topics at the Thanksgiving Dinner table), but no sane person would call it unity. And to carry on the merry way is to choose apathy toward the other, saying one is wrong but not doing anything about it. And yes, this actually happened in a church I know personally.
Second, a group of men are sitting around talking after Bible study. One glibly confesses porn usage "every so often" and keeps going in the conversation. The others shift uncomfortably because they fight their guts out to keep that poison out of their homes and eyes and lives. Unifying around Unity would say that everyone's an adult and should be able to do their own thing. So change the subject to baseball and keep on trucking.
But there's not true unity there. Saying nothing means porn is not a problem. Saying that everyone has to do what he has to do is a cop out and the same thing as saying porn isn't a problem. The only thing that unifies in a situation like that is to call for the godly standard of purity. Again, a true story with the names changed to protect the guilty (and innocent).
Relational Apathy does not equal unity. Thinking otherwise is self-deceptive and relationally destructive.
But that's just me thinking thoughts...