The way you phrase it, it sounds like a math problem (indirect or direct variation?), but I don’t think the relationship between apathy and discrimination is that straightforward. You said it yourself: on one hand, we have privileged people who are apathetic to social justice concerns; and on the other hand, we have disenfranchised/discriminated-against people who are just as apathetic. Therefore, it seems to me like what causes apathy is something other than privilege or the lack-there-of.
What I’ve always thought about apathy is this:
No one can care about everything that ought to be cared about in this world, which automatically means that everyone doesn’t care about something(s) they should care about.
Let me try again: the world is so big, too big for any one person, so we have to specialize in our engagement with it.
To provide a vastly-simplified example: if you care about rape victims, I care about needy rabbits, Joe cares about new immigrants, and Jane cares about clear-cutting, then we have 4 issues covered; but, if all four of us try to care about all four issues, likely nothing will actually get done because we’re stretched too thin, we can’t focus.
This isn’t just about time, physical effort, money – it’s about mental/emotional capacity, too. It may be obvious that none of us can save the world, but it’s just as true, and for the exact same reason, that we can’t even care about the whole world.
Not only that, but some of us are simply in a better position to look and care outwardly. For some people, it is a struggle to get through the day. If someone is using all their internal resources just to get through the day, they won’t have any left over to “care.”
My final point is this: long ago, in my first-year undergrad world religions survey class, I learned that in Hinduism there are 3 acceptable ways of engaging with the religion (and, thus, with the world/universe): studying/learning (using the mind), working in and with the community (using the body and social spirit), or devoting oneself to the spiritual aspects of the religion (using the soul, introspective parts of the mind, the psyche, whatever you want to call it). I don’t know much about Hinduism, and I may have misunderstood this principle, for all I know, but the lesson here is that it takes all kinds of people to make the world, and just because someone isn’t doing the good you’re doing doesn’t mean they aren’t contributing in a way you don’t understand.