One of the strongest parallels I find is that of religious tolerance and openmindedness. The concept that, while there is an absolute truth to be found, no one except God really knows what it is. In the case of Brandon's writing, that God would be the creator of the cosmere. He is the ultimate source of all truth.
Religions in general are fragments of absolute truth combined with interpretations, philosophies, and cultural mores of men. Often times religions are sects and splinters from other older religions that can change drastically over long periods of time, still retaining particles of truth, but with widely varying doctrines that may be far from the real truth.
Within the LDS religion we believe that we have more of the real truth than other religions do because we recognize that God continues to communicate with his children, through His prophets, and reveal new truths to us. But our prophets also continually warn us not be prideful or arrogant and to recognize the truths that other religions do embrace. If we are close-minded it becomes difficult to relate to others with differing beliefs and it also makes us less willing to accept new truth as it is revealed to us. While we are a missionary church that teaches what we believe to others, it should always be done in such a way that it enhances and adds to the truths that others already hold and respects the beliefs of others even if they differ from our own.
I see this very attitude strongly displayed in Siri and eventually in her older sister as they interact with the Hallendrans in Warbreaker. It is a strong theme in Elantris and the Mistborn Series as well. And while it hasn't blossomed fully in the Stormlight Archives yet, there are certainly passages, especially about Jasnah and the devotaries, that point to it and I think it will be a stronger theme as the series progresses.