Why should you call them on it? If their prejudice doesn't effect my personal relationship with that person to an appreciable degree, I could care less what they think.
Per Mrs. O, you call them out on it because you know they're wrong and for the sort of counter-intuitive sake of inclusiveness, actually. -- She says, basically, that alienating certain segments of society (by holding on to racial prejudices) isn't smart because America could need all its people to find ways to overcome important challenges of the future (like climate change, poverty, etc.).
BTW, her speech was excellent, imo.
I was amused by the part in her speech where she was talking to her young audience about how their views about racial integration were utterly unremarkable to them because of the times they've grown up in:
You have seen Latino singers win Grammys, black coaches win Super Bowls. You’ve watched TV shows in -- characters of every background. So when you watch a show like the “The Walking Dead,” you don’t think it’s about a black guy, a black woman, an Asian guy, a gay couple and some white people -- you think it’s about a bunch of folks trying to escape some zombies, right? Period. (Laughter.) Cracks me up to think about the first family watching The Walking Dead in the whitehouse.