Also while any individual bigot or misogynist may have specific mental health issues, so do those who are not bigoted or misogynist.
Plenty of people who would check out fine on a standardized assessment are bigots or misogynists. And plenty of people with all kinds of mental illnesses, injuries, and disabilities are non-hateful. (And victimized by bigots.)
Mental illness doesn't cause this kind of hate. It's a socially learned behavior arising from systemic values.