On a recent beautiful Sunday, I undertook an unusual experiment: I crossed a street.

I'm white and live in Oak Park, Ill., a surprisingly multicultural, upper-middle-class suburb of Chicago. The street I crossed separates my town from the city neighborhood of Austin, an almost entirely black part of Chicago. Though I often traverse it by car, I never have on foot. One day, I thought: Huh. Why not?

In fact, after last month's Supreme Court ruling forbidding the use of racial classifications to foster integration in public schools, we could all be forgiven for thinking that perhaps the races had integrated while we weren't looking.

Yet as I stepped over the curb, I became excruciatingly aware of my skin color, and my heart pounded with social anxiety. In going around a single block, I got stares. Mine was the only white face around, and for five minutes, five blocks from my home, I was a stranger in a strange land.

Of course, I'm that kind of white American for whom this shouldn't be true. I grew up in the 1970s, singing "We Shall Overcome" at school assemblies. I've had black bosses, written about Kwanzaa, and know what Juneteenth is. I even have a black cousin!

And yet, the line down the middle of that road might have been a wall. Created by fear, classism, or ignorance, I don't know. Am I conflating race with poverty, poverty with danger, the unknown with, well, the unknown?

I do know, vaguely, that Austin is one of Chicago's poorest neighborhoods, and by extension, a dangerous one. There's an unfortunately well-attended soup kitchen there, and Austin families often visit my neighborhood to play in its parks or go trick-or-treating.

But the block I walked reflects none of this. The stares I got were from a woman in a high-end SUV and a man on a high-end motorcycle. No matter our class status, I was out of place.

Moreover, and more to the point, there are black folks where I live, and I can't say that I know them any better than I do those in Austin. At parties or school functions, we chat and trade news; occasionally, we reference comedian Chris Rock or presidential candidate Barack Obama.

And at that very moment, that Chris Rock/Barack Obama moment, I become painfully, agonizingly, white. Beset by white liberal discomfort and mortified that I might appear to be trying too hard, I quickly change the subject, to something not identifiably black – teachers or taxes.

I wish I could ask the questions I would pose to anyone from a culture that is foreign to me. What do you think of Secretary of State Condoleezza Rice? Does the church's place in your community make it hard for atheists? What does white society – what do I – get wrong about you every day? I would ask these things of a German or a Pakistani. But I've never even asked my cousin.

We're not integrated. We're strangers.

What America needs is neither Supreme Court-sanctioned race-blindness, nor the Pollyanna "conversation on race," cited as a countermeasure when celebrities spout racist insults or Fox News mistakes black members of Congress. What it needs is to acknowledge the sheer distance between the races, and to make a real effort to bridge it.

I do not doubt that old-school racism remains a defining characteristic of American life, but I believe the kind of soft racism of which I'm guilty is part of the problem. So sure that my very whiteness puts me on a wrong foot, I won't admit our differences. So afraid of looking the fool, I learn nothing.

I hope that when my children read this 20 years from now, they'll marvel at my backwardness. That their experience in a truly integrated school system in which cultural diversity is a value both taught and lived will mean that my mental walls don't survive to their generation.

In the meantime, I believe I should try to get over myself.

• Emily L. Hauser is a freelance writer.