What is at stake is that the people in the church have become believers yet they act the same way they did before they believe. There is still in-fighting and there are still favorites. Focus is on the individual and not on what God does through the individual. Paul is stepping in because their actions now are becoming destructive in the community.
He reminds them that who ever they are around, believers or non believers they need to remain true to God's calling and presence in their lives. Paul reminds us that belief is not just something we talk about, it is something we live.