The religion hinges on whether a person can believe Joseph Smith's lifestory. He famously said, "You don’t know me; you never knew my heart. No man knows my history. I cannot tell it: I shall never undertake it. I don’t blame any one for not believing my history. If I had not experienced what I have, I would not have believed it myself. I never did harm any man since I was born in the world. My voice is always for peace."
He said this while being implicated in a conspiracy to assassinate the governor of Missouri, Lilburn Boggs. It is also a strange thing for him to have said at the time. He was nearly fifteen years into the Latter Day Saint movement, which he, Sidney Rigdon, and Oliver Cowdery founded. One would think that he would have confided with some of his close associates, unless of course, if they were in on the con with him. To me, that quote is more than a hint that there was a deception going on. Fawn Brodie, who was a niece of an LDS president, wrote a definitive biography on Smith and used that quote as a title. She was excommunicated for the content of that book. It would be interesting to know if she would still face church discipline given that her research has been vindicated by other authors, including the anonymously authored official LDS essays.
Here are a few links that I can think of at the moment:
Our subreddit FAQ has information about temple rituals. These rituals remain secret to members for at least one year after joinging. Many modern members do not know that the ritual originates in freemasonry and has been toned down in various ways, including removing gruesome death threats, nudity, possible groping. The ceremony remains extremely sexist where women must veil their faces at certain points in the ceremonies. They must also "harken unto the voice of their husband," whereas men promise to "harken unto god." Quote may not be exact. The whole ceremony is cloaked in secrecy and initiates do not know the content before they expected to swear oaths on the spot, without a chance to think it over in advance.
Evangelical Christians discuss part of a book, Mormon Enigma by Newell and Avery
Making the case for Joseph Smith as being guilty of statutory rape with enhanced penalties
These are the tip of the iceberg of what the average members do not know about their religion. Mormonism is a huge topic. The religion has a mainstream branch, but it also has a liberal branch The Community of Christ and a group of hundreds of fundamentalist splinters, many of which practice polygamy as defined by section 132.