To explain this, we have to understand how the subconscious works. Your brain is constantly registering and associating things without your input because you'd go insane if it tried to run everything by your conscious mind. Picture your subconscious as a secretary or assistant, making decisions that are so small or trivial that they aren't worth the boss's time. It's very easy to forget how extremely powerful the secretary actually is, just by virtue of all of these little decisions it makes day to day. And no matter how many "racism is wrong" messages you get in your conscious mind, lots of us still subconsciously make the connection between, say, black men and violence.
So even if you don't think you're racist, your subconscious secretary is still signing your name with a rubber stamp to some pretty racist ideas, simply because your neural pathways have decided that generalizing and stereotyping is a much faster way of doing business.
"Love your suit. Where'd you steal it?"
Of course, if you actually drink alcohol, your conscious inhibitions fall and suddenly you're screaming to a police officer about how Jews are secretly behind all of the world's wars. But since your brain is familiar with that process of inhibition, just being reminded of alcohol starts the process, if just a little tiny bit. You naturally become more relaxed, subconsciously remembering the no-holds-barred attitude you had the last time you were under the influence and screamed racial slurs through the entire game of beer pong.