Biblical fellowship is both vertical and horizontal. When we are saved, we are brought into fellowship not only with God, but with all others who share this same salvation in Christ.
They devoted themselves to the apostles' teaching and to the fellowship, to the breaking of bread and to prayer.
“All believers share a common life in Christ, whether or not we recognize it. We are in fellowship with literally thousands of believers from every nation of the world. Although we have never met most of them, yet we are in fellowship with them. We disagree with many of them over various issues of faith and practice, yet we are still members of the same Body. Even though we struggle to like some of them, that does not alter the fact that we share together a common life in Christ. Neither our attitudes nor our actions affect this objective sense of koinonia (fellowship). We are in fellowship with all other believers, whether we like it or not--or even recognize the fact. This objective truth of koinonia is meant to provide the foundation for the experiential aspects of fellowship. The realization that we do in fact share a common life with other believers should stimulate within us a desire to share experientially with one another. This is the whole thrust of New Testament teaching on koinonia." - Jerry Bridges, The Crisis of Caring