The primary purpose of the Body of Christ is to glorify God. Everything we do must serve this purpose, or we are doing the wrong thing.
- You are worthy, our Lord and God, to receive glory and honor and power, for you created all things, and by your will they were created and have their being.
- So whether you eat or drink or whatever you do, do it all for the glory of God.
The Great Commission (and I propose therefore the primary mission) of the Body of Christ is to spread the gospel.
The distinction here is important. Our mission to preach the good news needs to guide our actions, but allows for activities that don't directly impact this mission. On the other hand, any activity that doesn't glorify God should be rejected.
To illustrate, in a military unit I may be given a particular mission (let's say, to secure and hold an urban area in a combat zone). My ultimate purpose is to "support and defend the Constitution of the United States." I may participate in activities (eating, sleeping, training, morale building, etc.) that are more or less directly related to my mission. Moreover, there will be members of my unit (the chaplain, the medic, the cook ...) whose roles within the unit are more tangential to the mission than others (say, those of the infantryman, the intelligence analyst ...).
If I engage in activities that don't serve my overall purpose, I'm off course, even if they appear to serve the mission. For example, if I were to participate in a military coup, judging that a different civilian leadership would better serve my mission aims, I would be betraying my purpose for the sake of my mission.
In the same way, the church will engage in activities (worship, prayer, learning, acts of compassion ...) that may be more or less directly related to our primary mission of preaching the gospel to a lost and dying world. We also have members of the body whose particular gifts and talents (nurture, encouragement, teaching ...) tend to lend themselves toward these kinds of "support" activities, no less critical but less direct in their application to the mission of preaching the gospel to the lost.
If, however, in service of our primary mission, we sacrifice our purpose of glorifying God, we are off course ... we are sinning "for the sake of the gospel." For example, if a self-serving pastor seeks to grow a church in order to become wealthy and powerful, he sins. Though the gospel may still be preached and the lost saved, it is in spite of the pastor and not to his credit. In the same way, if the church were to depend on worldly methods (as opposed to trusting Christ) for the success of its ministry may seem to enjoy success, but because "everything that does not come from faith is sin," any glory to God is in spite of the church's actions, not because of them.
UPDATE: Please see the "Comments" for a great discussion on the definition of "mission", etc.