Schizophrenia is not 'extreme female brain'. It has an equal gender ratio, and the cognitive traits associated with it do not differ by gender.
I'm not convinced autism is an 'extreme male brain', but at least there's some evidence supporting that theory. For schizophrenia, there's nothing at all.
In contrast, there is good evidence of a link between autism and schizophrenia, since parents of autistics have a slightly higher rate of schizophrenia, and a large proportion of kids with childhood schizophrenia met autism criteria pre-psychosis. Also some genetic conditions have been linked to both conditions, such as velocardiofacial syndrome (22q11 deletion).