Star Trek V: The Final Frontier was almost universally panned by critics and fans alike because the movie told the story of Captain Kirk and crew following Sybok, a Vulcan mad man, to the center of the galaxy to find God. As the movie progressed, Sybok convinced more and more people that God was waiting for them at the center of the galaxy. Sybok and his followers sincerely believed that they would find God. They believed it with all of their hearts. They were willing to risk death crossing the Great Barrier into the center of the Milky Way because they believed so deeply. But when they finally arrived, "God" turned out to be nothing more than a convicted prisoner, sending out powerful telepathic messages to lure people in and then use their ship to escape. Sybok and his followers were sincere and devoted in their belief, but they were wrong.
In the story of Job, after God allowed Satan to destroy everything that Job possessed, three of Job's friends tried to help Job own up to the sin in his life, so that God would remove what they saw as a punishment from Job's life. One of Job's friends, Elihu, assured Job, "My words come from my upright heart, and my lips speak with sincerity what they know. The Spirit of God has made me, and the breath of the Almighty gives me life" (Job 33:3-4, HCSB). Job's friends were sincere in their belief that Job must have sinned to bring this disaster on himself. But Job's friends were wrong. God, ironically, had sent these disasters on Job because of his righteousness, not because of his sin.
At times, we can become convinced of our beliefs because of the sincerity with which we or someone else believes them. Sometimes we believe something so much, we just know it must be true. But being sincere doesn't mean we are right. Very often we are sincerely wrong. Many people sincerely believe that "God hates fags," but they are wrong. Many people sincerely believe there are ways to reach God aside from Jesus, but according to scripture, they are wrong. Many people sincerely believe that the Bible teaches that money is the root of all evil or that confronting people about their sin is "judging" them and therefore prohibited. But all of these people would be wrong.
No matter how sincere we are in our beliefs, we must be willing to reevaluate them when we discover evidence to the contrary. When we find something in scripture that commands us to warn people about their sin or we discover things in Genesis that don't read the way we thought they did, we must be willing to alter our sincere beliefs.
We can all be wrong, no matter how sincere we are. Our goal should be discovering the truth, not proving we are right.