1 John 1:7 (NIV) 7 But if we walk in the light, as he is in the light, we have fellowship with one another, and the blood of Jesus, his Son, purifies us from all sin.
Only as we walk in the light do we have fellowship with each other, as we do with Christ, regardless of geographical location or church membership. This is how the universal Church has fellowship.
We are unified through our association with Christ. Nothing else really unifies us.
It is only as we do His will (walk in the light) that we are purified from sin.
1 John 1:7 tells us that it is in the doing that we become Christ's.