The backwards radical
There is some confusion. Read Corey Robin's The Reactionary Mind and it will become much clearer. First and foremost, as the title suggests, the reactionary is a mentality. What he doesn't explain, as it's outside of his field of expertise, is that the reactionary mind is identical to what could be called the dark political triad (DPD): sociopolitical conservatism (SC), right-wing authoritarianism (RWA), and social dominance orientation (SDO).
A ton of research shows that, though distinct measures, these are overlapping traits. For example, studies repeatedly conclude that, under stressful and sickly conditions (pathogen exposure, parasite load, etc), there is a simultaneously increase across the population of the DPD traits, along with related traits like disgust response and traditionalism (real or imagined). This is explained according to the theory of the behavioral immune system.
It is ideological in the sense used by Louis Althusser's notion of interpellation. But DPD is more of a predispositional motivation that forms a larger framing of identity and worldview, before it expresses as any given social, political, and/or economic system of thought or set of values. That is the point that Robin is getting at, in stating reactionaries are hard to pin down. Umberto Eco made the same point in describing fascists as a loose constellation of descriptors, like the etiology of a disease ("Ur-Fascism").
So, let's be clear. Liberal politics comes out of non-reactionary liberal-mindedness (low in conscientiousness; & high in openness, intellectuality, fluid intelligence, cognitive flexibility, cognitive complexity, ambiguity tolerance, perspective shifting, etc). But as Robin explains, reactionaries have a talent for stealing from the Left. At this point, in terms of policies, almost every American is a liberal, since few care to defend the foundation of conservatism, that of classical conservatism: imperialism, colonialism, land theft, slavery, genocide, eugenics, bigotry, etc.
Reactionaries are shapeshifters, and so change with the times, yet they maintain their one and only principle that has two parts: 1) denial of the agency of the subordinate classes; and 2) defense of an entrenched hierarchy of privilege, power, and position. Leftism, on the other hand, was also founded on a central principle, that of egalitarianism which is the polar opposite of subordination to hierarchy.
If it ain't egalitarian, it ain't on the Left; no matter what rhetoric they use to obscure their intentions. This attempt to obscure is a defense mechanism of the reactionary right, as Robin details in his exploration of Edmund Burke's moral imagination. It's impossible to square the principles of the reactionary Right and the egalitarian Left, and hence it's literally impossible to have a genuinely reactionary leftist. Either they aren't a reactionary or they aren't a leftist.
That is where the confusion comes in because reactionaries have a talent for stealing leftist rhetoric and so can speak sometimes as if they supported egalitarianism. But you know their true nature by their anti-egalitarian actions (e.g., Stalinist state capitalists who opposed direct and democratic worker control of the means of production, the defining feature of communism).
Stalin was a reactionary who eliminated all leftists (real communists, socialists, Marxists, Trotskyists, anarchists, left-libertarians, labor organizers, free speech advocates, etc), and he did so in order to rebuild the Russian Empire but this time as an industrialized neo-feudalism where the serfs served the state. There was no worker control of the means of production in sight. What Stalin created was subordinated classes in an elite-controlled hierarchy, the complete contradiction of leftist egalitarianism.
This gets to Aaron Huertas "Reactionary Centrist." It comes to question about the 'center' of what. The center of elite opinion is pretty far to the right of the center of American public opinion. The majority of Americans are leftist on progressive taxation, corporate regulation, environmental protections, LGBTQ+ rights, same sex marriage, women's rights, abortion access, etc. Those posing as 'centrists' indeed are reactionaries because they are attempting to co-opt rhetoric to make themselves appear as what they are not.
See also Paul Kingsnorth invoking reactionary radicalism as the way forward.