Well, but whether the causes are genetic or organic or environmental, the observable symptoms are behavioural. (Introspective insights of the patient might be of some interest also but they are hardly very reliable.) Knowing the causes of schizophrenia is not essential to diagnosing it.
You are right that there is no meta-cultural definition of mental disease but, there is some reason to think that a person who behaves in ways that strongly defy the expectations of the culture they are part of, is mentally ill.
I don't agree with you here, as I very strongly find the expectations of this society quite mad, and I hope I behave in a way that comports this feeling. I know, for instance, that this society wishes to supress ideas and behaviour which it finds uncomfortable, and therefore would call people mad for merely thinking for themselves, and doing what they wish. It is as much, if not more, the fault of the culture, and not the behaviour of the individual, which breeds claims of madness.
I agree in part, at least I agree that the cultural / societal norms cannot be accepted as an absolute standard. There is a caveat that I find non-conformity more convincing when it is not immediately obvious or blatant, if you understand what I mean.
How do I feel about chess? With my fingers.