Obama's Church doesn't claim anything for being African-American. It says it's committed to Africa and their African heritage not only of African-Americans but also African ethnicities elsewhere in the world (other than Africa).
Unless they were born in Africa and immigrated to the US then they have no right to claim African American either.
I've said it before and I'll say it again, if your in the United States, then your an American, I don't care where your ancestors are from.
But just to play devils advocate, I checked out that church with an open mind, so if you live in Chicago and need to feel like God only see you if your in a church, theres nothing wrong with that one. They are not haters, so I can't say anything bad about them.