More on that conservative SF post
The more I think of it, the more I think that the premise of that post is based on the way we've stupidly defined politics in the US. We have just the two buckets labeled "left" and "right" and every single political term or concept goes in one bucket or the other and thus essentially becomes synonymous with every other word/concept/idea in the bucket, so right=conservative=libertarian=Republican=fascist and left=liberal=socialist=Democrat=communist… The concept is pervasive and insidious, so much so that our political discourse is reduced to seeing what kind of unpleasantness can we shove in the other guy's bucket.
It's a crock through and through.
Something as simple as the Nolan Chart starts to give a example of how much more complicated political ideology actually is. And even that is an oversimplification. There are way too many different axes of political thought to be confined in even two dimensions; and given the nature of SF, authors are often wont to play with these sliders in worldbuilding, often in combinations that are counter-intuitive. Here's a couple of those axes:
conservative radical
libertarian collectivist
anarchist statist
anti-authoritarian authoritarian
No these are not synonymous. Top down: first is the attitude toward tradition and social change in general, second is the primacy placed on individual rights in society, third is the role of government in society, and last is the level of trust placed in the elite powers controlling that society.