I honestly do not believe James's objection to Snape is bigotry against half-bloods (i.e. muggleborns are okay because they are a result of muggles doing what comes naturally; half-bloods are not okay because they are a result of miscegenation). But it's possible to read it that way if one wants to. It's not bashing; it's interpretation.
Considering that he bullies Snape four-to-one (or two-to-one at the very least) with the added advantage of an invisibility cloak and a magic map, and he woos Lily by means of sexual harrassment, it is not necessary to make out James to be a pureblood bigot in order to depict him as seriously un-likable. We HEAR good things about James in canon, but what little we actually SEE of him is just plain nasty.
I am a true Snape fangirl and can go into a good anti-James rant when I'm in the mood, but an anti-James rant is far too easy to be really enjoyable. Seeing him as having a prejudice against miscegenation adds a touch of complexity to him, but I know perfectly well JKR didn't mean it that way when she had James say he bullied the Half-Blood Prince because "He exists." She was just showing him as being thoughtless.
You think making an anti James rant is easy, well making an anti Snape rant is even easier. Let's see, sure James bullied Snape when he was a kid, but there is no way in hell Snape wasn't just as bad to him as well. I mean Sectusempra,we all know for who it was aimed. And don't tell me that while being a Death Eater Snape was all nice and cuddly. I think murdering and torturing people is a tad ( just a tad) worse than bulling. Also what we hear about Snape "oh he's so nice, he trully loved Lily". Yeah he was still a rasict and last time i checked being responsable of the death of a woman's husband( whom she loved) and her husband wasn't going to get her in your good grades. But what do i know about true love. The thing about James is that we see him in the books only through the eyes of Snape, so that might alter the perception we have on the character, because other characters speak highly of James. As for "he exist" I think he said it more out of jealousy that Lily was friends with Snape. As for this picture I interpreted it to be James teasing Snape because of his less than flattering looks than because of his blood. Because your theory that James is a half-blood racist doesn't hold up. He wouldn't have married Lily since he would have known they would have a half blood child ( aka Harry). It's like a racist white man marrying a black woman, it doesn't make any sence.