My best friend in high school was Puerto Rican and ours was an unlikely friendship. I was a terribly dorky and sheltered kid and he was vastly more well-rounded than I was. However we ended up becoming friends, it stuck.

Wandering around town (as teenagers do), I started to learn some very eye-opening lessons about some of our society's more subtle racism. Where his word was all that was required for his friends & family to accept me ("Nah, he's cool, man"), my family generally had a more difficult time accepting him. My dad shifted between being suspicious of him and using him as a sounding board for the justifications of his racist thoughts. My gramma would freak right the hell out when he would show up at our house (assuming that he was trying to break in), and the rest of my family simply used racist caricatures to make him the butt of inappropriate jokes. My friend was gracious enough to take this all in stride.

The time that I was really astonished at my own obliviousness, though, took place at our local Wal-Mart. We were wandering around the store, goofing around (again, as teenagers do). We ended up in the condom aisle, and because we were just immature enough that sex was absolutely hilarious, proceeded to laugh at nearly every word on every box of condoms. After the condom hilarity, we moved on to the fishes, which are, of course, pretty much right next to the pharmacy. At this point, I noticed that we were being followed by security. I shot a snotty glare that only a teenager can muster at the guard, and he seemed to back off. My friend warned me that I shouldn't do that, but I wasn't too worried. What was a rent-a-cop gonna do to us?

We go to leave about twenty minutes later (the fish were super interesting), but as we're about to walk out the door, the guard from earlier along with two other security guards stop us. They told us that we weren't allowed to leave the store because we didn't pay for "any of those condoms." My friend and I shared incredulous looks because neither of us had any merchandise, much less condoms. I informed the guard of this fact (I'm sure in the most polite and not at all assholey way), and he told me that I was lying. He then demanded we turn out our pockets and said if we didn't, we'd be detained until the cops show up. I then made a comment about how "real cops" didn't worry me, so he certainly didn't, because we hadn't done anything wrong and I was damned if I was going to be forced to prove my own innocence based on a mall cop's speculation (I know, I was a piece of shit). By the time I got done saying all this, I turned to my friend and was about to dramatically inform him that we were leaving, but I noticed that he had already turned out all of his pockets and was looking at me like I had just eaten a whole baby. He muttered "Shut the fuck up, are you crazy?" to me under his breath, and this made me even more indignant at the situation.

In the end, I created enough of a shit-show at the Gardening exit of the Wal-Mart that they just let us go without either calling the cops or forcing me to turn out my pockets. Once we were out of the store, my friend smacked me in the back of the head and asked me what was wrong with me. He told me how cops weren't my friend, much less underpaid security guards, and any "rights" I thought I had were all bullshit when it's just you and them. He couldn't believe that my parents neglected to inform me that authorities like that are dangerous animals which can only be soothed with enough "yes, sir"s and passive body language. I told him that I had actually been taught the exact opposite, that cops were servants of the public that have only a limited authority, especially if you knew your rights (or were an insistent little prick, at least).

This disparate perception of cops forced me to see that as a white person, I am usually given the benefit of the doubt at first glance, whereas my friend needed to work at proving that he even deserved that same benefit. Throughout the rest of high school, I was privy to many more first-hand observations of how the world around us treated him (a better student, more personable, more generous, better looking, etc.) in unfair ways that I never would have even thought of.

TL;DR: White guy become best friend with a Puerto Rican guy, which exposes the white guy to everyday racism he has the luxury of avoiding.

I'm not sure if you are specifically seeking anti-white stories, but this is the personal example of racism that stands out most defined in my mind.