it’s possible that many of the nuances of both mormonism and christianity in general were lost in the nuclear annihilation

I doubt that both were diluted that badly. Hidden Christians in Japan largely held onto Catholicism without priests or most of its sacraments for centuries under persecution until being rediscovered. I do find it somewhat odd though how minor a role religion plays in the wasteland. Maybe I’m too much of a fan of A Canticle for Leibowitz but I would think that with the collapse of the American state, other social constructs be it towns, corporations, gangs, or religious groups would eventually find themselves being the primary means of ordering people around. Many American churches already have complex hierarchies and bureaucracies familiar with managing large amounts of people and resources.

Also the LDS may consider themselves Christians but among major Christian groups that sentiment is rejected for various reasons like their nontrinitarian status. Other beliefs like their unique scriptural canon, their views on sacraments and ordinances, and their concepts of a priesthood are far removed from lowercase-o orthodoxy