The War on Terror, for instance.
I know it sounds like a rather oblique example, but actually racism can help explain many of the problems plaguing this seemingly never-ending war.
For instance, why did so many Americans support the war on Iraq to begin with, when it was pretty clear from the get-go that there was no credible evidence Iraq posed any threat to us and there was all sorts evidence to suggest Iraq had nothing to do with the 9/11 attacks? Obviously there were a lot of complex factors, but it certainly didn't hurt that Iraq, for many (most?) Americans, is a strange place filled with funny looking people, who even if they didn't have anything to do with 9/11 were probably still evil anyway.
But racism really helps explain why these wars drag on and on with no noticeable progress. Even bigger than listing the myriad ways American forces have blatantly ignored local cultures and customs, completely undermining the whole purpose of a "hearts and minds" style war, the inability (or unwillingness) to even understand the basic differences between peoples is clearly causing huge problems.
For instance, while U.S. officials continue to trumpet claims of capturing or killing important Taliban officials, it turns out many of these people aren't Taliban at all. In many cases, they don't even look like the people they're claiming (or claimed by others) to be. But hey, if all of these people look the same, who can tell?
And this, of course, is to not even mention the fact that many terrorists captured were for all intents and purposes simply invented by the government themselves. And again, while there's clearly many complicated factors behind these sorts of things, it's hard to argue that the reason these practices are accepted (or at least fail to produce any meaningful level of outrage) have nothing to do with the fact that they're really only affecting brown and black people who speak a different language and worship a different deity.
So even if you're a well-off white person who's never even seen something racist (at least, that you recognized), incredibly large sums of your tax dollars (not to mention thousands of lives) are being wasted, thanks in large part to racism.
[cue The More You Know jingle]