What is "racism"? What constitutes racism? Under what circumstances should a civilized, caring person call racism, and how should such a person respond to accusations of racism? I don't think there's One Correct Answer; I think the vagueness of the term calls for proportionate response.
In one sense, anything that has to do with race other than pure physical description or medical science constitutes racism. On the other hand, not all "racism" is tantamount to actual oppression and slavery.
Open racism — even the mildest — isn't generally condoned in the US. Even if you really are racist in a substantive sense, even if you consider black people or brown people or Jewish people to be typically inferior, lazy, greedy or whatnot, you can't just come out and say it. But after centuries, if not millennia, of explicit racism, socially and legally established, it would be egregiously stupid to believe that racism no longer exists.
One can define racism too far "up": You can't be called a racist unless you're seen to be whipping a chained-up black man while chanting "nigger nigger nigger". Nixon's Southern Strategy? States' rights, not racism. Welfare queens and strapping young bucks? Entitlements, not racism. Willy Horton? Crime, not racism. The Confederate flag? Heritage and history, not racism. Immigration? Border security, not racism.
It's bullshit, of course. Defining racism up is a tactic employed by racists who don't want to be called racists (and the occasional clueless fucktard) but still want to exploit racism for political power and personal gain.
So we pretty much have to define racism "down" and make it more general. But to do so, we have to respond proportionately. How egregious is the racism? What's the context? What's the intent? Just as carelessly bumping into someone isn't battery, a unintentional, mild racist comment or action isn't an endorsement of slavery. But similarly, it's still wrong, and merits an apology... and forgiveness.
Much of this analysis applies equally well to sexism, sexual orientation, national origin and other forms of discrimination.
I'm a straight white well-educated middle-class male from a Christian family. Name your social privilege, I've got it. I do my best to be feminist, anti-racist, non-hetero-normative, multicultural, diverse and sensitive. Do I fail occasionally? Probably. If I do, feel free to point it out. Just saying that I said something racist or sexist or whatnot is not going to make me want to hang myself. But I'm not going to cry about it, feel guilty, or invest hours in self-flagellation. If I fuck up, I'll admit it, apologize, do what I can to correct the mistake, and then move on.