The whole "Nazis are leftists" thing really blows my mind but I've seen people saying it unironically.

I really think The Reactionary Mind should be required reading by leftists. It really helps to understand why conservatism is actively opposed to individual liberty and how they sell these regressive ideas to a population primed for them:

Conservatism, then, is not a commitment to limited government and liberty- or a wariness of change, a belief in evolutionary reform, or a politics of virtue. These may be the byproducts of conservatism, one or more of its historically specific and ever-changing modes of expression. But they are not its animating purpose. Neither is conservatism a makeshift fusion of capitalists, Christians, and warriors, for that fusion is impelled by a more elemental force- the opposition to the liberation of men and women from the fetters of their superiors, particularly in the private sphere. Such a view might seem miles away from the libertarian defense of the free market, with its celebration of the atomistic and autonomous individual. But it is not. When the libertarian looks out upon society, he does not see isolated individuals; he sees private, often hierarchical, groups, where a father governs his family and an owner his employees.

No simple defense of one's own place and privileges- the conservative, as I've said, may or may not be directly involved in or benefit from the practices of rule he defends; many, as we'll see, are not. The conservative position stems from a genuine conviction that a world thus emancipated will be ugly, brutish, base, and dull. It will lack the excellence of a world where the better man commands the worse. When Burke adds, in the letter quoted above, that the "great object" of the Revolution is “to root out that thing called an Aristocrat or Nobleman and Gentleman," he is not simply referring to the power of the nobility; he is also referring to the distinction that power brings to the world, If the power goes, the distinction goes with it. This vision of the connection between excellence and rule is what brings together in postwar America that unlikely alliance of the libertarian, with his vision of the employer's untrammeled power in the workplace; the traditionalist, with his vision of the father's rule at home; and the statist, with his vision of a heroic leader pressing his hand upon the face of the earth. Each in his way subscribes to this typical statement, fromn the nineteenth century, of the conservative Creed: “To obey a real superior.. is one of the most important of all virtues- a virtue absolutely essential to the attainment of anything great and lasting."