This is a very interesting topic! Religious institutions has always been segregated. For example, many Chinese American Christians in Diamond Bar go to service at the various Asian churches at Hacienda Heights and Rowland Heights because a) the language barrier can be hard to break for new immigrants to attend a non-native language church b) usually the new immigrants are recruited by local faithfuls after arriving in the U.S. Guess which church are the Chinese speaking older immigrants bringing the new members to?
Then again, when culture meets culture, each will try to absorb the other unless the people are perfectly aware of our innate ethnocentrism and actively avoiding it, in real world that will almost never happen.
Even though I am not an active church goer, experience tells me churches and religious groups are not solely a gathering for religious activities only. Lots of times it is just another element of local social gathering where people can meet with like-minded fellows such as themselves. Since quite a number of people in each of the ethnic groups are first generation immigrants, then going to a church where it has their native language and customs would be a much more welcoming sight than one of another ethnicity (or culture). In the case for African Americans, racial issue is the barrier that segregates them from the caucasian churches (again, racial issues are often two way. I am not trying to imply "who discriminates who").
Caucasian/African American/Asian/Hispanic churches will stay that way as long as people feel uncomfortable with culture and customs that are unfamiliar to them (in this case, non-Koreans in the Korean Fellowship might feel alienated when conversations in Korean become frequent, or the members might be into Korean musics and movies that would be hard for the "outsiders" to enjoy).
I wish Prof. Allen from the Anthropology department visits this forum. He would do a much better job at explaining the frictions between cultures / religions / ethnic groups, in the U.S. or Worldwide.
Victor