The most common "I'm not a racist" equivalent phrase in American English is "Some of my best friends are [ethnic group name]". I think Kristina Lopez is probably much too young to have been around during the 1960s and 70s when this phrase was in vogue and the obvious "I'm a racist but trying to deny it" statement. I have no idea whether "I'm not a racist" is more or less common in Australian English than in other brands. Today's American racists say things like "It's time to take our country back".
Although I agree with Kristina that more "average" Americans are liable to keep their politically incorrect (PI) opinions to themselves in public, American politicians seem to have declared open season for the past 4 years and can't stop themselves from saying what they honestly feel, even if it is in code sometimes.
If you look at the reader commentaries in The Washington Post, you'll see lots of right-wing anti-Obama Americans refer to the President as "Barry" (that's one of the nicer names they use) and a host of other disrespectful and nasty epithets that they'd more than likely deny were racist if pressed: They'd claim that they're just exercising their 1st Amendment rights to be disagreeable about the government by expressing their purely political opinions. They're lying, of course. But anti-Bush left-wingers were no better during that guy's 8-year crusade. They were just as disrespectful. But they weren't particularly racist.
My opinions above are based only on what I read on the Internet, what my American mother who still lives there says to me when I can't prevent her from talking to me about US politics, and what I hear from my American friends and acquaintances here in Taiwan (they go back to the USA every year. I don't).
(DISCLAIMER: I don't live in the USA, so I don't get involved in its politics and have no preferences about who runs the country. As far as I'm concerned, it doesn't matter which party's "in power". The major corporations and the lobbies with their money run it for their benefit, which is what happens everywhere else in the world, so why should it be different in the USA?)