With the assumption that there is systematic racism, you need a descriptive term for racial minorities. I'm more inclined to say "racial" or "ethnic" minority, because it immediately states that I'm referring to a person's status as a person holding less power in the system. I don't find POC offensive as much as I find it redundant when "ethnic/racial minority" is more accurate and more specific to why you'd be using a race/ethnicity-specific term.
As for "black," as Lisa said, I prefer to call myself black and others who are subjectively "black" at a glance, because it's usually a simple, descriptive term for the two races with the most significant influence in America in the past decade.
Heck, I've even heard "brown" person used by the politically correct and politically incorrect, because that's more specific to the acknowledgement of the "model minority" of Eastern Asians and how it differs from racism seen by black, Latino, and Middle Eastern/Indian people in America.
It doesn't really bother me by itself. As long as they're not discrediting the cause of feminism in trying to acknowledge systematic oppression (which is already a hard sell,) they can use whatever commonly used term. The argument behind it will show if you're legitimately informed about social justice issues, a trendy social justice person looking for excuses, or an ignorant STEM dude or bipolar lady thinking they're supremely knowledgeable about a field of study they've never studied.