We've seen a lot of bigotry in the Harry Potter series before. Draco Malfoy calls Hermione a Mudblood, meaning that she's a magic-user with non-magical parents. Then there's the Death Eater "prank" at the beginning of Book 4, when they levitate a Muggle family through the campground at the Quidditch World Cup because they enjoy torturing Muggles. But the hatred in Harry Potter and the Order of the Phoenix has a slightly different character.
Professor Umbridge hates half-humans, so she also has racial prejudice. But her hatred is largely aimed at people who disrespect her authority. Professor Umbridge loves rules. When she first comes in to the classroom, she insists that the students answer her with a full, "Yes, Professor Umbridge" or "No, Professor Umbridge." She wants them to show their obedience to her at all times. And when a student – ahem, Harry – doesn't immediately obey her, she turns the most terrifying loathing onto them. The thing is, Professor Umbridge's name is notably close to "umbrage," meaning to take offense. Everything offends Professor Umbridge, and she hates anything that offends her. So, by association, Professor Umbridge pretty much hates everything. And her hatred sours the whole atmosphere of Hogwarts throughout Book 5.