Very simple I guess: I don't.
Unless the other person insists I do. And then somehow I cannot repair the damage done. As an individualist and libertarian I first look at each person as an individual until their own words or actions say "put me in this group" (not just race¹) or "my group identity is more important than our relationship". Then that is how they are filed in that great filing cabinet of my mind.
This segues into something that has bothered me for a few days. A young(?) man who was a regular contact on my Flickr account, who mutually traded comments about railroad photographs, his and mine, found a photograph that editorialized on my feelings about the upcoming changes in our medical system, and left me a rabid disagreeing comment. I responded with logic, gently compared to here, and he left me a scathing reply about why I was wrong about the lack of individual responsibility and malpractice suits as lottery being real problems that aren't even being addressed; and he then promptly blocked and banned me from any further contact. It is a shame, I liked his photographs, and he mine; but he could not tolerate someone having dissenting thought. How far we as a culture have strayed from Voltaire's words in his Essay on Tolerance: "Think for yourselves and let others enjoy the privilege to do so too."²
Now, having said that, What would you do? If you came into your child's classroom and found this posted? It is an extremely racist work of I believe student art, although there are no other student works posted in the classroom, at all. So far, I have done nothing, said nothing, probably will not, and this is the first I have publicly mentioned it. But one standard I have always considered is: "If you reverse the parties, would it be offensive? Then it is offensive both ways". But what if you came into your child's classroom and found this prominently posted, what would you do?
¹ I had a correspondent on the internet who was profoundly deaf (don't expect hearing impaired from me). I ultimately stopped writing because the sole focus of her existence was her deafness, like that really was an important attribute on a computer bulletin board.
² The phrase "I disapprove of what you say, but I will defend to the death your right to say it" is widely attributed to Voltaire, but cannot be found in his writings. With good reason. The phrase was penned by a later author as a description of his attitude. It appeared in The Friends of Voltaire (1906), written by Evelyn Beatrice Hall under the pseudonym S[tephen] G. Tallentyre.