The integration into the Right of anti government and anti authority ideology as a virtue is one of its worst corruptions.

Indeed. Whatever the dominant ideology is within any given physical space pulls all lesser ideologies also within it in its own direction. For example, nationalism in a liberal society becomes warped into a civic nationalism which compatibilizes it with less extreme forms of liberalism. And conservatism in a liberal society becomes warped into the liberalism of that society but with a few years or decades removed. In effect, everything simply becomes a branch of liberalism and lesser and less a full-fledged ideology of its own.

That particular general anti-government, anti-authority ideology has far more in common with anarchism and Marxism than with what Americans call paleoconservatism, which is why it seems senseless to call libertarianism genuinely 'Right-wing'. If we define 'Right-wing' as anti-authoritarianism itself, as libertarians are wont to do, then anarchism becomes Far-Right rather than Far-Left, and we are left with a totally nonsensical political spectrum.

For me, America has never had an actual Right-wing: after all, it was America's very Founders who came up with what now tends to be called 'libertarianism'. The term that they prior used, liberal, was simply taken from them by the far more powerful 'progressive' strand of liberalism, and hence those whose liberalism was trapped in the time of the Founders needed a new label to go by.

"The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants" is perhaps one of the greatest quotes of that ideology. I would add to what you have mentioned in your second paragraph, that anti-authoritarianism is for these people an end in itself. They don't see liberty as a means towards something substantive like a potentially higher level of creativity, and they do not see the lack thereof as a means towards something substantive like consolidating social structures. Instead, they dogmatically defend liberty even when it harms them, as in the case of all the 'woke' nonsense clearly being justified and enabled through liberal dogmas. It is similar to how some libertarians endlessly go on about a decline in theistic belief and how 'one nation under God' isn't really a thing anymore, woefully unable to understand that it is precisely their very own value of liberty that allowed people to choose to reject theistic belief in the first place.

The libertarian cope for the phenomenon of 'wokeness' is essentially to posit that its cause is precisely the opposite of what it is: no longer is 'wokeness' a consequence of excessive liberty; it is a consequence of some sort of Communist/Fascist tyrannical plot to destroy liberty. So, rather than accepting progressivism as being a descendant of, or innovation on, their own ideology, they predictably choose instead to lump it in with their old time enemies. Their worldview is essentially that progressivism is also right up there with Communism, Fascism, and more illiberal conservatisms like American paleoconservatism, that is, as enemies of liberty. Of the four ideologies I mentioned, they will never accept that the pursuit of liberty actually has a strong causal role in the creation of both progressivism and Communism. I think the only difference between them is that, unlike libertarians, also accord a high value to equality, and much of the 'tyranny' involved in the two is the consequence of the inherent mutual contradictions between the two ideals, i.e. of the free society and the equal society. When the latter prevails over the former as is often the case, then you indeed have a tyranny in practice: wealth redistribution and so forth necessitates a large government.