Because "liberal" is too old and historical of a word to successfully pervert it's meaning. It dates back to the enlightenment, that's how old and established it is.
But many other terms are more recents and haven't become derogative. Ecology is strongly left-themed and actively fought by economical powers, and yet it's never become an insult, and even the ecology-themed insults (like "tree-huggers") have rather backfired than took on. More significantly, "feminism" is very close as a core ideology, and it's been subject to attempt to smear it for quite a bit longer than "woke", and yet somehow it has quite a bit of staying power as a political badge, and even tends to be used as derogative only insofar as it's, precisely, close to the "woke" ideology (this latter point is especially noticeable in France, where "feminism" is a much more widely used label than "woke", and tends to suffer more from the "woke" stigma).
I think that woke often means "bad left" (or to those who think left bad, just "left").
I disagree, "woke" as I've mainly seen used, refers to a specific aspect of the left/far left, that is strongly tied to identity politics. It's not about "bad left" in general. There is a significant difference between a select subset that is seen as bad by itself, and a subset that covers everything that is bad.
Whether left and right are also bad terms or not, I don't think woke is that useful regardless (because no, I don't think people know what they're talking about when they use it, generally).
Dunno. I don't think people "knows better" what exactly entail "left", "right" or "neo-liberal" than they do about "woke". I find all these terms to be equally useful.
But to put it bluntly, rather empirically, it has been the case, several times. Somehow, some undercurrent (or overt attempts) by the right to coopt and misappropriate left language has worked, a lot. This is baffling because there's no real illuminati; there's alt-right who remain hidden and quote god forsaken Dragon Ball memes as part of their internal discussion, but they're still relatively few, even if having become more prominent recent years. Then there's stuff like Fox. Can they do this? They're not supposed to be able to - the left has tried to direct language to become more healthy so many times, but ineffectively - and yet, we've seen it happen by the right, over and over again.
I'm afraid I simply don't have experienced the same. This might simply be due to the fact that I have little contact outside of Internet with the political right (I have a few friends and acquaintances that I suspect vote right/extreme-right, but they are dwarfed by the amount who are left/extreme-left, and even then they are more of a "personal vote" kind of people, not politized at all), but I've actually felt the opposite. Nearly every word that have seen its meaning changed, nearly every change to the vernacular coming from political roots, have come from, precisely, the "woke" subgroup (again, this is especially noticeable in France due to French being a gendered language, and there is a whole battle happening on how to alter the grammar to make it more progressive).
Can you give examples of terms that have been twisted and misappropriated ?