Here are some very interesting reflections on the church growth's homogeneous principle, the idea that people are most attracted to groups that are like them. The idea has been used in the past to justify mostly white, black, or Hispanic congregations that are not very diverse.
Bob Whitesel has cleverly suggested that there is even a sense in which multi-ethnic congregations can be homogeneous in the sense that they usually attract people who most enjoy a multi-ethnic setting. He also argues that the homogeneous principle was never meant to exclude and that it applies best to subgroups in a congregation rather than to an entire congregation.
I don't think there is a one size fits all answer. Any church that does not look like the community in which it is located should probably do some self-examination. Certainly no one should be unwelcome at a church and a church should do everything it can to be welcoming to everyone in its context.