A lot of non believers are willing to go along with some church in their lives because they think their TBM family members are that important. Sometimes they are in transition to being fully exmo.
They don't always get a lot of respect here, where many of us like to think it was pure courage that got us fully out. In fact, it is a lot easier to leave if your beloved TBM spouse isn't freaked out.
I thought it was Name Only Mormon. As in an active participant, but non-believer. The reverse of a jack-mo (inactive believers). New Order Mormon brings to mind a person who is actively trying to reform the church from the inside.
MINO ~ Mormon In Name Only is what you're thinking of. Acronyms are sometimes difficult. IHA ~ I Hate Acronyms for example. But they can be useful when understood by all.