Like the Avenue Q musical says (sings)
Me: It depends on what you mean by racist.
If you mean that we all hold attitudes about racial groups, and that some of these attitudes are negative (as the Avenue Q song implies), then yes.
Attitudes we have about groups are cognitive heuristics, and these are usually both useful and justified (The Unbearable Accuracy of Stereotypes: http://www.rci.rutgers.ed
We have attitudes about groups all the time - it's just that some of them are more socially acceptable than others. For example, we assume that lawyers make more money than construction workers. Sure, the odd construction worker might make more money than the odd lawyer but overall the stereotype holds. So if I were meeting a construction worker for lunch, I wouldn't suggest going to Morton's Steakhouse (a famously expensive joint).
Given that many people of the same racial group have something in common, attitudes about racial groups are also justified. For example as someone of East Asian descent I was taught by my mother how to use chopsticks, and I would assume that most others of East Asian descent would also know how to use chopsticks. However, the same sort of reasoning is just as true for women, Seventh Day Adventists etc.
Race is, then, just one of a large category of classifications (including gender, class, sexual orientation, religion and many more) with which we make sense of the world, and which helps us interact with others (once we know more about them, more relevant individuating information about them comes into play - the previously linked paper talks about this).
People don't usually have a problem with positive stereotypes, but the flipside of positive stereotypes is negative ones. For example women are supposed to be more caring than men, but the flipside of this is that men are more heartless. So even if one concentrates on positive stereotypes of racial groups, one is still being racist.
So yes, once again everyone is a little bit racist, because that's how we make sense of and interact with a complex world.
Ironically, the people who rail about racism are usually themselves also racist.
Take the popular accusation of "privilege" - it assumes that the "majority" race inevitably benefits compared to "minorities", and compensates by vilifying it:
HENRY. Do you know what you can say? To a black man. On the subject of race?
CHARLES. “Nothing.”
HENRY. That is correct.
(pause)
CHARLES. Black people can talk about Race.
--- Race by David Mamet
In closing, here is a line I like from Bruce Hubbell's answer to Obama First Term (2009-12): Why has Obama lost support among whites?:
"President Obama got a lot of votes from people based on the color of his skin. Many people wanted to elect a black man president to send a message about race relations in this country. They also wanted to be perceived as "color-blind" when it comes to race. So the only criteria was his skin color."
I'll let you reflect on the irony of wanting to be seen as colour-blind and yet voting based on skin colour, and what that says about colour-blindness, racial attitudes, racism and racial discourse.