As long as I'm sincere in what I believe, isn't that enough for God?

Sincerity is important. Peer pressure and a desire for acceptance are poor reasons to follow Jesus. God doesn't ask us to fake it; He desires a free and sincere obedience.

But sincerity should not be confused with truth. I can sincerely believe that the earth is flat, but I will still be sincerely wrong. Since all of my decisions will result in real consequences, I want to base my decisions on the best information possible. Walking off a 100-foot cliff will result in great pain, regardless of my personal belief concerning the law of gravity. If Jesus is the Son of God, if He really is the source of life and fulfillment, then I really do rob myself of joy, peace and deeper growth by walking away from Him. Our response should be sincere, but it needs to be based on truth.