I never see any of these people care about the mentally ill or trauma victims unless it's sexual assault which can be pinned on the patriarchy.
Plenty of the SJ movement is focused on mentally and physically handicapped people - its part of why I've started to notice plenty of people railing against those who look down on autistic people and why ableism is becoming more and more cared about.
As far as trauma victims, I'm pretty sure that there is a reason that many people who discuss particularly traumatic events preface their discussions with trigger warnings - to prevent people who suffered rapes, abuse (sexual, physical, mental, what have you) from being blindsided.
I will agree with Mathias about wealth being probably the ultimate "privilege" though. It is part of why I'm beginning to question my faith in capitalism as a functioning economic system because it inherently creates massive gaps in which there are people who have excess in all areas and those who have absolutely nothing at all to their name and likely never will.
One thing that people forget though is that racial minorities (especially blacks) face MUCH higher rates of poverty in the US. Part of the reason for this stems from years in which black Americans post-slavery were not able to easily obtain property and as a result had nothing they could hand down to their children and their children's children.
The odds are stacked against them because of our racial history.
Crime rates are higher amongst minorities because of the essentially institutional poverty - when you remove effectively all hope of them ever bettering their lives you instill a criminal mindset, and no not all people turn to a life of crime and yes people do escape from their bad situations, but generational poverty exists and it exists for a very real reason.