If one really wants to use the "blood status as race and blood supremacists as white supremacists" metaphor, then we have to grapple with what that actually means for the HP narrative as a whole, not just when it supports an argument. Because you can't fix the issues without understanding the fullest extent of how such a metaphor would affect the narrative.
Unsurprisingly, using blood status as a metaphor for racism turns out to have a variety of problems:
Muggles would be POC, Purebloods would be white, and Halfbloods would be mixed with white. There's no model for being mixed without white or there being more than two races ... unless you want to assign some people a literally nonhuman status, which can be damaging in itself.
Muggleborns, who have been theorized to be descended from squibs marrying muggles, would then (by implication) be poc theorized to have distant white ancestry, proof of which suddenly pops up in a descendant. This ancestry is their ticket into a secret magical world.
White people would almost always get superpowers, and it's genetic - your children usually get superpowers if they're part white. If a white child doesn't have them, they'll be pitied at best, and sent away from their families to live amongst people of color.
Voldemort AND Umbridge are both biracial, while Bellatrix is crazy, and the Malfoys get a last minute defection, because gods forbid sane white folks be depicted as the driving force of racist movements. Snape and Dumbledore are also biracial, and Snape definitely didn't pass for white as a child while Dumbledore might have, which makes their roles as ex-racists get really odd. Also Milicent Bulstrode, the Slytherin who is specifically shown to be more physical than most of her female classmates (using her fists) and is put on Umbridge' Inquisitorial Squad? She's revealed to be biracial outside the books, too. Harry would also be biracial, but be stated to look like a clone of his white dad and barely anyone ever wants to talk about his mom. His dad's friends seem to know little more than her name and eye color.
Metaphorically, there'd be a period of history where a bunch of random people who seemed white were burned alive for presumed superpowers.
Petunia would literally be the trope of the mean woc who hates her better, prettier, whiter-seeming sister out of envy.
Snape is repeatedly described as ugly in part because of the nose he shares with his muggle father, whom would be a man of color under this metaphor. Said father is all-but-stated to abuse his wife and son, which is hinted to be in part for them being metaphorically white and half white, respectively. Outside the books, the father is stated to "not hold back with the whip", a greater degree of physical viciousness than any other abusive parents in the series.
And these are just the immediate issues which spring to mind. I've no doubt there are more.
I intensely dislike when people just equate pure blood supremacy = racism. Drawing a parallel isn't wrong but they aren't equivalents. In some ways it is more similar to class, but above all its a fictional system of oppression. These will always have elements of similarity to real systems of oppression ofc, but its not a book series about racism that uses different words.
Theres so many things about pure blood supremacy that don't translate to racism.
There is no real life equivalent for the difference between muggles and muggle borns. Muggles are people who don't have magic, but that wizards have oppressed because of this, muggle borns are people with magic, that wizards feel shouldn't have it (or at least shouldn't use it). Wizards legitimately have power over muggles regardless of discrimination. None of this has a parallel in racism at all.
The history is very different. It seems that the wizarding world has kind of always been relatively accepting of muggle borns, with a few hard-core blood purists, quite a lot of semi accepting people (for example fudge is shown to have some of these ideals but not want people thrown out of the wizarding world), and some people who adamantly are against pure blood superiority. I say this because the founders o hogwarts had this exact conflict 1000 years ago. Seemingly Slytherin failed at getting them to not accept muggle borns, and there doesn't seem to be a point where that changed. There's nothing in the books that suggests there is any history of widespread slavery of muggle borns or anything even remotely similar to the history of racism. As above, there have been periods of time where muggles sought out and tried to kill wizards, for which there is no precedent for racism.
Half bloods are closer to pure bloods than muggles or muggle borns. Dumbledore, Harry, Voldemort, Snape are all examples listed above. None of these people seem to face significant discrimination for their blood status. Voldemort takes over the fight of the pure blood supremacists, and Severus gets pretty high up in these ranks. Dumbledore ofc rises to notability on the other side. We follow Harry throughout the whole series and exactly once does someone chastise his blood status (Bellatrix). Hermione, on the other hand, is consistently insulted for her blood status, and there exists a specific slur for people like her. So while pure bloods are the ideal, and half bloods presumably face some oppression for not being pure, they are kind of pure blood adjacent. This is the opposite if you think half blood = mixed race. Having a white parent may bring some advantages in life, but ultimately if one of your parents is a person of colour then so are you.
Most wizards are half blood. This is established in chamber of secrets. The rarity of full pure bloods is what makes me think of them as more like billionaires or royalty than white people. Further than that, muggles are a massive majority of the population.
It also just really creeps me out when people will aggressively stan the likes of bellatrix specifically because of how evil she is, but then turn around and simply equate pureblood supremacy with racism. Imo its fine to feel that way about characters like Bellatrix, she's not real and neither are her victims, but if you think of her as like the second in command of like the KKK or something then... wtf... even if the details are still fictional making it out to be a book about racism really sheds a very bad light on stanning the villains.
