But hate crime is specific to an outlook or pattern of behaviour. That's almost a definition of what separates it from crime that is not hate-related. It's a crime triggered by the criminal's assumption that they have the right to attack because their victim is 'Other,' that the victim somehow deserves the crime because of their otherness.
Racism is an outlook and pattern of behaviour. Racists automatically assume someone of a different colour, creed or religion is inferior to them, has no place in their society, deserves to be ridiculed, bullied, sidelined, should show respect and know their place and be grateful for crumbs and be extra polite and not assert themselves or be too visible or be openly different from what the hate-criminal determines as 'normal.'. Any progress made by people from the targeted race is seen as positive discrimination or wokery gone mad, rather than an acknowledgement of the person's abilities.
All of these are equally relevant to misogyny, aren't they? Is there a significant difference?