>someone without schizophrenia to correctly perceive schizophrenia.

This has little to do with bias, and more to do with the fluid nature and standards we use to diagnose these conditions. If you look at a DSM or similar diagnostic catalog, over the years, you'll notice that the criteria for diagnoses change. This is a result of learning more about the condition - but at the end of the day, there isn't a simple, mechanistic diagnosis for most mental pathologies.

In the case of schizophrenia, we can't say If you have a protein level <X, you have schizophrenia. It comes down to a number of subjective symptoms, and how the patient experiences them. That's not bias, that's simply not having a clear cut definition for a condition.

Combine this with the fact that many conditions that are considered distinct have similar or overlapping symptom profiles, despite having potentially different causes and potentially different responses to therapeutic strategies.

Emotional bias in research is not the biggest problem. The biggest problem is that defining a clear cut mechanistic cause for these conditions is exceptionally difficult.