An LDS publisher recently requested to see a rewrite of my novel. (Hang on. Is that "An" or "A" LDS publisher? I'm going with "An" since it sounds better.) [Say it aloud and use the one that fits.] Obviously they haven't offered a contract, but for the sake of fantasizing, I'm going to pretend they will. Since I don't live in Utah, how will this affect the marketing of my book? For example, book signings, school visits, etc. Also, are LDS publishers wary of taking on authors who live outside of Utah for this very reason? Thanks in advance!
Since the huge majority of LDS books and products are sold in the Utah/Idaho corridor, living somewhere else means you won't have easy access to multiple promotional signings. It also means you won't be able to do co-op events with other LDS authors--like workshops or community events or Ladies Night at Deseret Book before conference. Unless, of course, you're willing to drive/fly out for a week or two and hit all the bookstores who'll have you. (That will probably not be paid for by your publisher, so think about taking a working family vacation.)
If there's an LDS bookstore in your area, we will set up a signing for you there and at any other local bookstores that will let us in. If you're going on vacation to an area that has LDS bookstores, we can try to set up a signing. You can also do RS workshops or firesides locally and within neighboring wards/stakes.
You're on your own with schools, as is every author. Living in Utah doesn't mean an automatic pass into the schools. It depends on the type of presentation you'll give, the content of your book and your connection with the school.
Pretty much anything else can be done regardless of where you live--thanks to the magic of telephone, fax, Internet, and good 'ole USPS. Radio shows, book reviews, websites, blogs, online interviews, press releases, postcards, catalogs, etc. can all be done no matter where you live.
So, no. Publishers won't turn you down if you live outside Utah as long as you're willing to make the effort and do what is within your ability and budget to help promote your book.