>>498I think you're right that this is a question of epistemology. Here's my take on it:
An opinion is a hypothesis, which can either be true or false. The goal of any discussion must be to approach the truth. This is most efficiently achieved by eliminating hypotheses which are demonstrably false.
For example, two people are arguing about the shape of the earth. One claims that it's cubical, the other that it's flat. Together, they work out testable consequences and predictions which must follow from their opinions (both agree that it must have at least one edge). They agree to travel in one direction. They discover that they end up where they started and that no edges have been observed. Both opinions are rejected and they work out that the earth is probably a sphere - until they discover that its rotation makes it an oblate spheroid. Rinse and repeat.
What I'm getting at is this: Useful opinions are ones, which produce testable claims. Bad opinions are untestable. If there is a black/white scenario like the one OP describes, work out the predictions of both sides and see which (if any) holds up to facts.