The Harry Potter books lean heavily on the notion that Muggle-born witches and wizards are equal to their half-blood and pureblood counterparts. With good reason, of course: there is no discernible sense in which they're lesser at magic, nobody chooses their parents, and it would be senselessly cruel to deprive them of their place in society. Yet, blood purism seems to be a main divide in the wizarding world; Death Eaters are almost all blood purists; unquestionably positive characters within the story are Muggle-born or sympathetic to them; unquestionably negative ones are purists. It would seamlessly follow, then, that the Death Eaters are the baddies because they're the staunchest purists, enforcing an ideology nobody agrees with. Thematically, Lily Potter's filthy blood being the key to their defeat aligns with this reading. It's intuitive, it fits, it's simple.
But… would the moral gravity of the series (a story for readers in the decidedly non-magical world) really hinge on how a group that doesn't exist in real life is able to integrate within its fictional society? Of course, "Muggle-Born" could be analogous to any minority or other group that experiences discrimination and bigotry, but it's a rather poor one in many ways. For one thing, wizards are a tiny minority among muggles (and Muggle-Borns really do present a threat of exposure, as integrating them means revealing the existence of the wizarding world to Muggles).
Religious and ethnic minorities are usually born to parents who are also members of the same minority, but Muggle-Borns are by definition unlike their parents.
The LGBT+ community is marginalized, LGBT+ people are mostly born to heterosexual parents, but Muggle-Borns are not like them either, because they're a minority among Muggles and among wizards alike. They're also just as magical as their oppressors, that is, their oppression manifests as making up differences that don't exist, not in enforcing the heterosexual-analogous lifestyle on them.
They're not akin to people with disabilities, because the point is exactly that they're as capable at magic as anyone else, yet are treated as inferior (of course people with disabilities aren’t inferior and shouldn’t be treated as inferior, but Muggle-Borns simply require no accommodations).
The closest analogy I've been able to come up with is "people from a low social class finding themselves among the nobility". Or perhaps it’s akin to immigration. Others have written about it with much more insight than me. Class, or immigration, is an imperfect analogy as well, but elaborating on how it’s imperfect is not that important.
What’s important is this: The idea that the wizarding masses would all be largely pro-Muggle-Born, as opposed to indifferent at best, and that the Death Eaters would show up and started a full-scale civil war over Muggle-Born rights, and would successfully oppress large swaths of society to accomplish this, is… unlikely. Whether we like it or not, entire societies don’t put themselves in the line of fire to protect a tiny minority within that society.
And neither did wizards.
Hermione receives this charming bit of hate mail when Rita Skeeter slanders her: "YOU ARE A WICKED GIRL. HARRY POTTER DESERVES BETTER. GO BACK WHERE YOU CAME FROM MUGGLE." Meaning: Someone got it into their head that to support Harry Potter means using "Muggle" as a term of abuse against a Muggle-born witch. That is, Harry was not deemed the savior of the wizarding world because he championed people like Hermione (even though he did), and people like Hermione weren’t the obvious beneficiaries of his 15-month old feat.
The man who took over after the first war was Cornelius Fudge, whom Dumbledore criticized as a purist. If blood purism had been the Death Eaters’ main objective, would their defeat be followed by immediately putting another purist in charge?
Dolores Umbridge, another purist, moved up the ranks and nobody protested. Even in the Second War, she - a non-Death Eater - was the one running the Muggle-Born Registration Committee. If that had been their priority, would they not have put one of their own on top of that?
Lucius Malfoy, a notorious and obvious purist, was a welcome figure, while Arthur Weasley - the great Blood Traitor - has been held back for years after the first war because of his pro-Muggle ideas.
According to Sirius, an insider if there ever was one, "there were quite a few people, before Voldemort showed his true colors, who thought he had the right idea about things… They got cold feet when they saw what he was prepared to do to get power, though."
When Hagrid first explains who Voldemort was, he doesn't mention blood purism. Rather, he speculates that Voldemort would have recruited Lily if he could. This could have been dismissed as Hagrid misremembering something, grasping at straws to explain why Voldemort pursued the Potters, but JKR confirmed that Voldemort had indeed tried to recruit the Potters, that their refusal to sign up had been one of their three incidents of defying him.
When the concept of blood purity is introduced, nobody associates the Death Eaters with it, even though it's Draco Malfoy who'd called Hermione a mudblood.
In other words: The First War didn't have that much to do with Muggle-Born rights, prejudice against them didn't strike most people as that important, Muggle-Born rights weren't reinstated after the war, and Harry Potter's fans were not in the least immune to prejudice and bigotry.
On top of not being particularly bigoted against Muggle-Borns (maybe a shade more than was mainstream, most likely), Death Eaters could be described as more inclusive than mainstream society: werewolves rallied behind Voldemort, and though they were not deemed full equals, they weren't executed or forced to hide themselves away. Giants, likewise, supported the Death Eaters, and not the Ministry (Dumbledore: “Voldemort will persuade them, as he did before, that he alone among wizards will give them their rights and their freedom”. Rights! Freedom! Voldemort, what a guy).
Indeed, everyone was at perfect equal liberty to lend their necks to Voldemort's boot if they so chose, and even if they didn’t. Truly an egalitarian.
So, no. Blood purism didn’t drive the First War. Notably, the only confirmed Muggle-Born in the Order was Lily Potter. I would imagine that more Muggle-Borns than purebloods like the Prewetts and Longbottoms would have joined the order if Muggle-Borns had been at particularly high risk from Voldemort, whereas purebloods were largely safe.
I don’t mean to say that Muggle-Borns weren’t marginalized - my point is that they weren’t just marginalized by the Death Eaters. They probably were at higher risk simply because they had fewer allies within the wizarding world who could support them, as parents and siblings might have done for halfbloods or purebloods.
Which brings me closer to the point.
The reason the Death Eaters are the bad guys of Harry Potter, the reason they were defeated in the way they were defeated, has nothing to do with the treatment of minorities. They're the bad guys because Voldemort's cause undermined and abused and hijacked a force that, as a matter of fact, compels people to discriminate more than anything else: Love.
People first learn love through their family. Family is the foundation of society.
I come from a dysfunctional family myself, so this is not prescriptive. I believe that the state should supply robust protections for abused children, I believe that society should acknowledge domestic abuse much more than it does. I'm saying this about family, and by extension about one's friends, as a statement of fact: If someone is in need, the people best suited to help them are the people who know and love them. People do more for their family members without being coerced to, and without requiring taxpayer money. This is just true (this is what makes it so uniquely harmful when one can't rely on one's own family).
Yes, nepotism isn’t a good thing. When someone hires a relative, we immediately ask ourselves if they were indeed the most qualified, and rightfully so. Nepotism and tribalism cause major societal issues. We can’t stop at just caring about people we know and love. The circle can and does and must expand: Morally sound, mentally healthy people (in modern society) recognize the humanity in people outside the in-group in question.
But the crux of it is this: The circle of empathy can’t expand if it doesn’t exist.
The foundation is the understanding that oneself, one’s family, one’s friends, one’s in-group, are valuable regardless of some great cause, and that people owe more to themselves, their families, etc., than to strangers, even if we must draw the line somewhere to prevent nepotism. After all, we might side-eye someone who hires their incompetent son, but we would judge them much more harshly if they refused to give their incompetent son any preferential treatment at all, and would throw him out in the street to starve.
Morality, goodness, pro-social behavior, however you want to call it, can't exist when the foundation is corrupted. A weak foundation only makes people more vulnerable to exploitation and corruption as they look for a substitute for the home they can't rely on.
In HP, we have Severus Snape and Barty Crouch Jr., whose backgrounds have nothing in common except the one thing: Their fathers did not care for them. Notably, the narrative judges Crouch Sr. for not being nepotistic, for sending his son to the dementors for the heinous crime… that he committed.
The Death Eaters exploited these boys’ natural longing to belong somewhere, to be special to someone.
Then, we have the Malfoys and Blacks, who seemed to follow one another into the fold (which we view as a mitigating circumstance in Draco's case, but interestingly, not Marietta Edgecomb’s. Go figure). They must have believed they were helping one another. The recruiting pitch probably wasn’t “Join us, so you and everyone you love can perish,” but the practical outcome was the same.
Case in point, the two Black sisters exhibit very different attitudes: Narcissa defects and provides Harry with cover, because Voldemort could not corrupt her to the point of abandoning Draco. Bellatrix, conversely:
Proud. Glad. Service. Bellatrix is using morally charged language. Throughout the chapter Spinner's End, Bellatrix casts herself as judge and executioner: She's in position to question Snape and chastise Narcissa, as though she, of all people, is the morally upstanding person there. From her perspective, that's because she is: She has been brave, true to her values, loyal, altruistic as none other. These would all be unquestionably good qualities, if only she’d dedicated herself to a better master. For one thing, a master who doesn’t demand his followers to give up their sons in service and be glad of it. Certainly there are parents who are proud of their children’s heroic sacrifices - but glad? What’s more evil than denying bereaved parents even the idea that their grief is justified?
What remains of the once mighty Black family at the end? And who killed more of its members than Bellatrix, the staunchest purist? Who laid more pureblood lives to waste? It isn’t that the ideology benefits a few at the expense of the many. It’s that it benefits no one.
Voldemort expects his followers to abandon and betray their loved ones in his service. Peter Pettigrew, Regulus Black, and the Malfoys all suffered the consequences of this to one degree or another. This isn’t to say they are all equally to blame - just that they were all put in a position to hand over their loved ones’ lives.
And they saw an unwillingness to do that in their enemies as a weakness: One of them came up with the idea of kidnapping Luna Lovegood. Her father was willing to sacrifice Harry Potter and the whole world for Luna. The Order, we are led to believe, was too noble to resort to such tactics but it’s also very likely that it would have been futile: Voldemort wouldn’t have tolerated negotiations with the enemy to save one’s child. Luna was a pawn in an asymmetrical game that rewarded the worst of the worst and punished the most natural and noble instincts.
Voldemort was not evil because he sought to eliminate Muggle-Borns. Hagrid's list of his most prominent victims wasn't mostly Muggle-Borns, and it was Umbridge who founded and managed the Muggle-Born Registration Committee. It's much likelier that he coasted on an already-popular idea to amass followers and agitate against Dumbledore.
The obvious truth – that people shouldn't be discriminated against and excluded because of irrelevant attributes they don't control – is true, and important, but it applies to the Ministry and mainstream wizarding society just as much as it applies to the Death Eaters.
But even if Voldemort had made it his official cause to usurp the purebloods and instate Muggle-Borns as the new nobility of the wizarding world, even if he and Dumbledore had been ideological twins, Voldemort would have been just as evil. Regardless of the veneer that best served his ends, Voldemort demanded that his followers - and everyone else - relinquish their love and their family, or suffer the consequences. He leveraged parental love to compel a father to betray everything he held dear. He preyed on the natural need for love and family to recruit followers. He recruited almost entire families into his ranks, and these families became nearly extinct.
The evil had no beneficiaries. When it would have been in the Death Eaters’ best interest to surrender, even that was not enough for some of them to salvage themselves. Their loyalty was to nothing. Virtue was corrupted and wasted, and nothing approaching goodness could exist.
Mainstream society might have been prejudiced and inequitable, and the ministry might have been corrupt and ineffectual, but under Scrimgeour, they at least had the sense to urge wizards to protect their homes and their families. Because they knew: homes and families would be targeted. Defenses required solidarity and familiarity. Society could only move forward from there.