A huge question for people who no longer believe in the tenets of the LDS church is whether to keep the rules of the Word of Wisdom. The WoW, in a nutshell, states that members are forbidden to imbibe alcohol, coffee, or black tea. They also are not allowed to smoke or use recreational drugs.
Some non-believing members continue to live the WoW because they don't see any need to partake of the forbidden substances. Some abstain because they don't want others to see them with a Starbucks cup in hand and then judge them (yes, drinking coffee is a major sin if you're LDS--it would keep you out of the temple and would probably get you released from your 'calling').
Some non-believing members decide that it's fine to "responsibly" indulge in coffee, tea or alcohol. Some even smoke sometimes or try a bit of pot or X. Believers may see this experimentation as further proof that the unbeliever is under the influence of Satan. They see the forbidden substances as a mechanism for Satan to gain control of their bodies (i.e. if you're addicted to coffee you're losing your self-control, or if you drink alcohol you are more likely to have cloudy judgment which will lead to greater sins).
Mormon scripture on how Satan works:
And behold, others [Satan] flattereth away, and telleth them there is no hell; and he saith unto them: I am no devil, for there is none—and thus he whispereth in their ears, until he grasps them with his awful chains, from whence there is no deliverance. Yea, they are grasped with death, and hell; and death, and hell, and the devil, and all that have been seized therewith must stand before the throne of God, and be judged according to their works, from whence they must go into the place prepared for them, even a lake of fire and brimstone, which is endless torment (2 Nephi 28:21-23).
So those who are no longer believers, but who desire the trust and respect of their LDS friends, are caught in a bind. Indulging in forbidden substances offers proof to their LDS friends that they are under Satan's influence. The result is that it's very difficult for the unbeliever to retain trusting relationships with believers. So that cup of coffee or that sip of wine or that beer at a football game--while seemingly benign and socially acceptable to almost all Americans...may permanently damage lifelong relationships for those who are or were members of the Mormon church.