If Christians worship the same God, why can they not put their theological differences aside and cooperate actively with each other?
Because when a religion focuses on "belief", then they tend to consider intellectual assent to be central. If the intellect is central, then the doctrine becomes more and more specific over time. The Protestant Reformation caused a stretching of this (after wars and centuries), but the habit of narrowly defining doctrine is a habit that is hard to break.
Many Christians feel that doctrine has become a burden, and it must be lightened. However, now the question becomes WHICH doctrines should be considered less significant? That's the stage Christianity is going though now, and it is a difficult process. Suppose someone took your most prized values and said, "That's not so important." It just doesn't feel good.
But it is true that Christians need to work together. The kingdom of God should be changing the world, and as long as we are separated into different buildings, different ideologies and different organizational groups, we will not work together to do what is important: feed the poor, love the outcast, heal the sick, and show Jesus' love to all.