Certain churches, like Greek Orthodoxy, have a strong cultural element to them that is divorced of the religious element. Have you ever met someone that identified as a secular Jew? It's the same concept.
It's sometimes - probably not in this case but that's not the point - a little different even to that, at least in places (or within subcultures) where the social pressure to attend Church (or whatever) has collapsed. Obviously that's not a massive issue in America, but not totally alien I think.