It's unclear what prompted Palin to call President Obama out, but it could have been a squirrel or a rock she saw on the sidewalk. (And even if he had played the race card, in his defense, Palin has ALL of the crazy wild cards and she's still not winning hearts.) "Playing the race card" refers to accusing people of racism as a strategy to gain clout. But maybe we don't accuse people of racism enough. Martin Luther King Jr was committed to ending the racial divide, but doesn't exclude calling people out for being racist at all. In fact, it kinda relies on it, like a space ship does on an engine or a nerdy feminist does on bangs. Ending the racial divide isn't as simple as pretending racism doesn't exist, because racism is not made out of the same pixie dust as Tinkerbell.
Once I was at a bar (because duh) watching a comic on stage. My friend said, "I like him, but all his jokes are about being black. He's using it as a crutch." I responded, "Aren't all your jokes about pizza and masturbating?" Referencing racism does not mean someone is using racism as a crutch.
When conservatives accuse people of playing the race card, it implies racism is over, which it isn't. Whether or not
there's less blatant public cruelty to people of color, they're still systemically disadvantaged as far as education and jobs. So when people like Palin say, "I just don't even see color anymore," it's like, maybe get your eyes checked because your glasses should be for more than making you look like a less hot Tina Fey.
When President Obama says there is racism in our society, he's not begging for sympathy, he's empathizing with others, which is an admirable and beautiful quality in a leader.