My MS is gradually approaching the point where I would like to share it with a critique group. However, my home is a thousand miles away from the epicenter of LDS publishing.
My question is this: Would I be better off meeting with a local critique group who may not be familiar with the church and the LDS market, or should I try and find an online group of other LDS writers to work with?
A local critique group will give you real-time feedback. You can ask questions and get answers immediately. You can hear the intonation they use when they make comments, see their facial expressions, hear them snicker in appropriate places (or not). That type of feedback is very valuable. While online groups can give you good feedback, you don't get to see or hear that immediate emotional reaction to your writing.
If you can find a local group without religious bias that is willing to work with you, that is your best bet. The fact that they may not be familiar with LDS culture is not necessarily a negative thing. If your writing is clear enough that non-LDS readers can understand the LDS concepts without feeling preached to, and they can relate to the universal human emotions and experiences that are also part of your story, then you've done some good work.
If, however, you can't find a group that is open to religious writing in general, and/or LDS writing in specific, then your only option is online. Which is not to say that online critique groups don't also provide a valuable service to the writer. They do. So don't feel bad if you can't find a local group.