'Padmasambhava said that when a stick is thrown to a dog, the dog will chase the stick. A dog’s gaze follows the object, the stick. The lion gazes steadily at the source, the thrower. We need to look at our mind, the source of the emotion. An emotion like anger is the stick. The source hurling that emotion is our mind. It is the mind that projects. The source of our experience is our own mind.
Dzogchen [Buddhism] turns our gaze inward toward the source of experience, which is mind. Pristine mind is our lion's gaze.'
But it's important to acknowledge there's a huge difference between singleton one-off insults -- where it's easy to take a "sticks and stones" attitude -- vs. being immersed in an environment where you frequently hear insults from a wide variety of people around you. Which also inevitably comes coupled with equally if not more non-verbal slights, ranging from the subtle and physically harmless (locking car doors, being followed by store security guards) to the economically painful (statistical disadvantages in the job market or justice system) and even physically dangerous (e.g. the recent spate of police shootings).
Not being a minority I can't directly identify with that experience, but I have to imagine the "laugh it off" argument doesn't really apply well to a life filled with such experiences.
Here's my tip - when someone does or says something that hurts you, examine why you feel the way you feel and treat it with amusement. I'm a minority that has dealt with racist comments. It is what it is. Do the words hurt me? No. I'm amused at how ignorant some people can be, and I move on with my life and write some code.