The only unforgivable sin, apparently, is blasphemy.
Morality is not tied to the bible, and I do no one any harm by not believing their claims. Not sure what your definition of what is and is not moral, but no sane definition could consider this so. It is prosecution of thought crimes, lol.
Realistically, the bible draws its authority from itself. It says that there is a god that made it, and that god's authority keeps it awesome, even though it is the only proof for that god. Not sure if I would see that as a reliable source for moral teachings, or teachings of any kind.
I cant think of any reason why its bad. Should we believe in god though every piece of evidence tells us hes not real? That kind of intellectual dishonesty is one reason ive come to despise religion. Id say believing in god and doing whatever your gods (leaders) tell you to do is wrong because its not god who wrote these religions its flawed people. While your at it (doing your gods will) why dont you support communism or facism. You can see the flaws with these only because you havent been raised to think theyre perfect and you dont add words where they dont exist to make it say something good where it literally says something bad like you do with religion. Dogmatic religions equal atrocities and without them where would our belief in god come from? So no i think its good to not believe in god. Too many people kill torture and enslave for god. Fyg.
The question itself begs yet another question. Does a god or gods exist to believe in? Until there is some real evidence that such a supernatural being of any kind does or ever has existed disbelief in the default proposition. Anyone who's taken and intro to statistics knows that the null proposition is always default and any other must be supported by data. So no, disbelief isn't a sin, it's logic.
If god did provide free will, then why should there be a negative consequence for doing what is allowed (if it is truly allowed)? If the choice is indeed free, there should be no negative consequence associated with it. Assuming god exists and the Bible is true, it would seem non believers are being coerced into belief when considering the threat of hell.