Well, I disagree that "privilege" needs to be eliminated entirely from the social justice vernacular. I think it just needs to be explained better and contextualized in a more honest way.

I'm cisgender, White, and male (although gay rather than straight). I would argue that I enjoy privilege that Michelle Obama doesn't, in many areas of life -- due to my racial category and my biological sex. However, I definitely believe Michelle Obama enjoys privileges that I don't -- due to her sexual orientation, her current socioeconomic status, and just her all-around iconism (celebrity privilege). She and I share the same gender identity status (cisgender), so the comparisons between us there would be a little less pronounced.