That's not even CLOSE to a real quote from Squidward's Labor speech. The others are all direct quotes, why couldn't we get a pull?
Hufflepuff are collectivist, but also nativist. They're for toleration, but only among those they consider "their people". Consider, for example, how they treat Harry. They're perfectly content to support and befriend Harry as long as aligns with their interests (i.e. beating Slytherin), but the instant he is established in opposition to their tribe (e.g. when he becomes the 2nd Hogwarts champion), they turn on him savagely. It's also fairly easy for Hufflepuffs to fall into "greater good" sorts of thinking.
I'm not thinking of how Hufflepuff students act in the books, I'm thinking of how the values of the house are portrayed. The Sorting Hat's songs consistently portray Hufflepuff as above the trait-based (meritocratic) "sorting" of students into houses, and willing to teach any student regardless of purity, honor, or intelligence. Further, the ideal Hufflepuff is always portrayed as a loyal and salt-of-the-earth laborer.
Again, as with perception of Gryffindor being heavily colored by Harry, who has some very distinctly non-Gryffindor tendencies in the way he takes action, a lot of Slytherin's perception comes from Voldemort and the fallout which follows his defeat. Just because Voldemort is Hitler and the Death Eaters are Nazis, doesn't mean Slytherins are authoritarian, right-wing nativists by necessity.
Salazar Slytherin himself, and the entire house's ethos, is built around purity of blood and nobility, the most auth-right of all the houses. Voldemort and his followers always embodied this, yes. That doesn't disprove the characterization.
Slytherins tend towards a very strong individualism; accomplishing things on their own, by their own faculties, and without having to seek outside help (think Draco's mission to kill Dumbledore where he bristles at the thought of Snape or his mother bailing him out). Even Voldemort doesn't really see any of his allies as anything more than pawns to accomplish his ambitions. He may develop a Nazi-esque credo, but this is little more than a justification he crafts a posteriori to justify his already-existent sadistic interests.
None of this contradicts characterization as auth-right. Within every fascist movement, personal achievement and supremacy has come only second to purity. The struggle to be the one who succeeded in the eyes of Voldemort is comparable to be the one who succeeded in the eyes of Hitler, or any other dictator.
Being in the inner circle of the focus of the personality cult is definitive of status in fascism, and this is what all the Death Eaters fought for.
To Voldemort, the loyalty of his followers is sustained by some power dynamic and nothing greater. He is, in a way, the perfect realization of a Randian ideal. An Übermensch who starts from nothing, achieves untold power and wealth solely through his own abilities and maintains no loyalties and sentiments but to those who provide some tangible material or political benefit to him personally. And he's perfectly content to discard or destroy them as soon as they cease to provide this function to him.
It wasn't solely through his own abilities, though, as we can see with the flashbacks to his own childhood he had the same sort of cult of personality based on purity of the blood and right-wing violence that any fascist does. The Death Eaters were mostly schoolyard bully types, much like Riddle himself, who were attracted to the air of violence and supremacy that Voldemort represented. The ideological basis for his rise was the same as that of any fascist: appealing to a crowd of not-really-victimized people who think they're victimized by some scapegoat group (the pureblood Wizarding families, by the Muggle-borns and the Muggles) because of the liberalization of society and the widening of civil rights. Using shows of force to ensure that purity and righteousness will return the reactionary follower base to power.
Think of Umbridge, for example. She wasn't attracted to Voldemort out of any sort of reverence for his abilities or admiration, it was solely due to his actions and message that she became loyal to him. The return of pureblood wizard supremacy, the authoritarian power of the state, the violence to maintain these things were the appeal for her, and indeed for followers similar to her. Only his direct inner circle was composed of the weirdly loyal, like the Carrows and the Lestranges, whose loyalty came from a place of derangement and was absolute rather than conditional based on his power at the time, and this is also reflective of the historical fascist regimes.
Slytherins are fiercely loyal, but only to those whom they would consider their "people", and "people" for a Slytherin is decided very rigidly on a case-by-case basis, as opposed to a Hufflepuff who categorizes broadly in tribes.
The Huffelpuff students are no more or less guilty of this than other students, while the ideals of their house are all about solidarity. Meanwhile the Slytherins fight for popularity, status, and appearance, belonging to a house with ideals based in purity and strength-- and "ambition".
Consider Malfoy with Harry. Malfoy is extremely willing to befriend Harry early on (this even despite him being the catalyst for the destruction of Voldemort), and it is only after Harry declares himself an enemy to Malfoy that Malfoy begins to treat him that way. If that's not right-wing libertarianism (a rigid individualism in which everything must be accomplished by ones own ability and faculty), then I don't know what is.
The myth of the superman is, aside from one particular writer, more widely associated with the fascist ideas of the auth-right. The strength and purity of the base of support for a movement, and of its leader, has never been associated with right-libertarianism outside of Ayn Rand, who is something of a joke in my experience. It's a shame, because I think she's right about a lot of stuff.
The reason I'm juggling on whether to put Gryff or Ravenclaw in authoritarian/libertarian left is because Ravenclaws are individualist, while Gryffindor are collectivist. But Ravenclaws are also big on a constructed idealism that could lead rather logically towards a Bolshevism or Maoism of a kind. It's hard to see Gryff as collectivist because their most prominent representative in the source text is Harry, who has very strong lone wolf/individualist tendencies, which I would argue come more from his Slytherin secondary.
The real meat of right-libertarian ideology is the devotion to (their brand of) logic. Individualism, in its true form, independent of the ability to amass followers or feats of violent strength, at the intersection of economic autocracy, is ideally all about rewarding the most intelligent or capable of reason. The extent to which the ideals of Ravenclaw as a house are discussed in the books is generally that the most intelligent or clever are regarded above all else. This fits in nicely with the holier-than-thou narrative of right-libertarians.
Meanwhile Gryffindor, with its focus on honor and defending the weak, seems to nicely reflect vanguardism or general auth-left faith in the ability of the right group of ideological custodians to serve the proletariat.
You should read the books. The Sorting Hat tends to characterize each with one word: Gryffindor are brave, Slytherin are ambitious, Hufflepuff are loyal, and Ravenclaw are clever. Through flashbacks and historical dialogue we learn more about each house and its founder; particularly that Gryffindor was thought of as protective of the Muggle-borns, and a fierce fighter but with little understanding of their actual desires, Slytherin was a racial purists and wizard supremacist, Ravenclaw was a sort of detached and elitist intellectual, and Hufflepuff was a jolly and personable but also hardily inclusive and tolerant idealist.