Harry Potter is, largely, a story about power and privilege. These themes show up in different ways throughout the series, the biggest way being the relationship between wizards and Muggles. Ironically, it is also one of the most complicated relationships in the books, because the lines between power and privilege between the groups are extremely blurred and dependent on the situation.
On first look, it seems as though wizards would be the ones who have both power and privilege over Muggles. They use magic, which, while it can be seen as an equalizer among magical people, grants those same people more power over non-magical people. On a physical level, wizards can easily overpower Muggles (as long as they have their wands). The Wizarding World is also deeply engrained in pro-wizard rhetoric. While being pro-wizard doesn’t automatically mean being anti-Muggle, the rhetoric does tend to advocate for isolationism and exhibit patronizing behavior towards Muggles. On its own, it can be virtually harmless, but when engrained in the structures of wizard society, it can create distrust and dislike of anything Muggle or of people who are more interested in Muggle way of life. This is exhibited in Order of the Phoenix on page 72 when Fred Weasley tells Harry that the Minister of Magic, Cornelius Fudge, thought Arthur Weasley was a “weirdo” for his interest in Muggles and that Percy Weasley told his father that he’s had to struggle against Arthur’s reputation since joining the Ministry. A part of structural power is being able to affect people’s livelihoods based on their beliefs or identities, and in this instance we see that this is exactly what Fudge does. The Weasleys are poor in part because of Arthur’s Muggle obsession, and while Fudge doesn’t necessarily call Arthur a “blood traitor,” it’s clear by his actions that he feels that someone with Arthur’s proclivities make him unworthy of a higher position within the Ministry.
By far the most extreme example is that of the overt anti-Muggle and Muggle-born rhetoric and the obsession with blood purity, generally voiced by older, “pure blood” families like the Malfoys, Gaunts, and Blacks. Even here, there are levels to the bigotry. On the one hand, Blaise Zabini is disgusted with Muggles and Muggle sympathizers, calling Ginny Weasley a “blood-traitor” when speaking about her (Half-Blood Prince, 150). However, he does not come from a family of Death Eaters like Draco Malfoy. Sure, Blaise was taught that Muggles and Muggle-borns were inherently inferior to wizards, but he wasn’t taught to go out and murder them. Even the Malfoys aren’t at the far end of this spectrum – on Pottermore, we learn that the Malfoys actually had dealings with Muggles in the past, especially in financial capacity, which is how they built their wealth. One of their ancestors was even a suitor to the Queen. But the Malfoys are known for being a family of opportunists. When it was clear that wizards favored isolation from Muggles, they became the top advocates for “keeping the bloodlines pure,” and their descendants, namely Lucius Malfoy, ended up serving the greatest Dark Wizard of all time. The most extreme of this spectrum, obviously, are the Dark Wizards who believe this rhetoric to the point of mass murdering Muggles and terrorizing the wizarding community into doing so as well. Salazar Slytherin is notorious for being anti-Muggle, and even created a secret chamber and monster for the sole purpose of murdering those he saw unfit to learn magic (read: Muggle-borns). Gellert Grindelwald (along with Albus Dumbledore initially) believed in ruling over the Muggles “for the greater good.” He terrorized Europe until Dumbledore himself had to go and stop him. Lord Voldemort was dedicated to furthering the work of his ancestor Slytherin and terrorized both the Muggle and Wizarding Worlds for eleven years before being defeated by Harry Potter the first time, and three years after he came back into power. These are all very serious situations and lends to the idea that wizards hold the most power in their relationship with Muggles.
But then things get more complicated. There are a bunch of wizard laws in place to make sure that Muggles don’t discover the existence of wizards and an entire governing system in place that works for the sole purpose of keeping the secret. The wizards are less in voluntary isolation from the Muggles so much as they are in hiding. The International Statute of Secrecy was put in place in 1692 because the wizards were being terrorized by Muggles. At a time when wizards and witches (and falsely accused Muggles) were being persecuted and burned at the stake for their use of magic, the wizarding community had to come together to protect themselves. Rather than going into an all-out war, they hid. Though wizards do have magic, they were vastly outnumbered by Muggles; in the UK there are only an estimated 3,000 wizards.
While Salazar Slytherin definitely went too far, his initial reason for not wanting to accept Muggle-borns into Hogwarts was because of his mistrust of Muggles (Chamber of Secrets, 150). After being persecuted and attacked for years, it’s only natural that he would be wary of allowing the offspring of his attackers from infiltrating the very place where young wizards grow up and learn to use their magic. And while many witches and wizards were able to charm themselves into not being burned when they were persecuted for being magical, it was undoubtedly a terrifying experience (unless you’re Wendelin the Weird), and undoubtedly many witches and wizards were killed during the witch burnings (Prisoner of Azkaban, 2). You need only look to the Dursleys for a more modern example of how some Muggles would view magic to see that the wizards are in hiding for a reason. It even says in Harry Potter and the Prisoner of Azkaban that the Dursleys “had a very medieval attitude toward magic” (2).
In the end, it seems as if Muggle terrorism begat wizard terrorism, complicating the idea that it is the wizards who hold all of the power. Throughout the Harry Potter series Muggles are constantly depicted as unsuspecting, in need of protection, weak, and oblivious. They are also affected by things happening in the wizard community – including the fall of Voldemort, Sirius’s breakout, the Death Eaters breakout, the Quidditch World Cup, and more. While we don’t really get a glimpse into whether this also happens the other way around, it’s safe to assume that large events in Muggle history also affect wizards, no matter how isolated they are. The power held by both seems to be more of a balance, sometimes tipping in the other’s favor, and complicated either way.