One of the pieces objecting to the concept is titled "you could be a racist and not even know it". This is, in fact, the point. For the most part, racist talk is unacceptable in our society now. But many people say things that are offensive in their ignorance, even if their intention is not to be hurtful. Someone saying you only got into your college because you're black is pretty racist, but "where are you from" as a coded question about your ethnicity is still hurtful. I only get asked that because of my unusual name, and even then, people ask where my name is from, not usually attributing qualities to me. Because I'm "white".
The conservative objection is that people who are angry all the time need to toughen up. That the world isn't always nice and taking offense when none is intended is just making things difficult, and censoring the rest of us. I think a good counter point to that is this comment:
I had a day yesterday that speaks to this so perfectly. First I had to listen to my male coworker - who never shuts up - try to teach me about my own job, then I had to listen to a male faculty member "teach" me (I'm a univ. librarian) about research in his area (already knew 99% of it, but he acted like I was just born), then my male boss decided to blab to me about parenting (I have 3 kids, I know the drill), and finally I get home and my husband blabs to me endlessly about why the Cosmos show is so important and that if I understood astrophysics like he does, I would agree with him etc etc f-ing etc. I felt like screaming and/or running away by 9 pm. I AM SO SICK OF MEN TEACHING OR TRYING TO TEACH ME SHIT. But wait, if I get fed up and react at all, I am just a hormonal wench who can't control her mood(s).This is from an article about how women are harassed and insulted whenever they show expertise in a traditional male area. Music, computers, video games, carpentry. "Let me carry that for you." The point being that the occassional offensive or hurtful remark should be something you can shrug off, but when you get it from everyone, every day, it adds up. People who are being hurt are speaking up, telling the oppressor to shut the hell up and no you can't touch my hair. And there's nothing wrong with it.