The challenge I've encountered is coming up with a word to describe the culture that surrounds the membership of the church, but which does not give the false impression that such cultural features are institutionally sanctioned.
For example, books like "The Work and the Glory" used to be referred to as "Mormon fiction." But if that word is no longer acceptable, and calling it "fiction of the Church of Jesus Christ of Latter-day Saints" gives the wrong impression, then what do we call those books? And this is an issue that goes beyond fiction: Mormon film, Mormon taboos, Mormon rites-of-passage. My daughter just had a movie party with her friends last night and watched "Monty Python and the Holy Grail" for the first time. That's a "Mormon rite-of-passage, but definitely not a rite-of-passage of the Church of Jesus Christ of Latter-day Saints.