How?

Nothing was proved either way.

No, no that didn't. Just because someone denies an adverse position doesn't mean that they are fanatically denying evidence, it can easily be the case that the adverse position is false, and that they are open to seeing it proven true but haven't seen it.

Perhaps a better question would be: Consider two parties starting out relatively reasonable. Over time, members of both parties claim the other party is becoming unreasonable or outright crazy. This could be true in the following to scenarios:

(1) Both parties have become crazy. Both parties would be correct in their claims but of course also guilty of having gone crazy.

(2) Party A has stayed reasonable and party B has become crazy. Party A would be correct in their claim and party B's claim would be part of them being crazy.

How do you distinguish between (1) and (2) from the outside?