It’s a broad label for anything they don’t like (LGBTQ+, feminism, DEI, etc.), but doesn’t “woke” mean you are awake? Would that imply that things that are not “woke” or are “anti-woke” are “asleep”?
Then they go on about conspiracies (“climate change is not real”, “deep state”, “5G is harmful”, “vaccines cause autism”, the list goes on unfortunately…) where they’re claiming that you need to “wake up to the truth”. Surely they don’t consider “woke” to be “the truth”, so shouldn’t they call it something like “asleep”, “sleepy”, “snoozy”, or similar?
I needed to use a lot of quotation marks there…
As others already wrote, the original meaning has been specific to awareness of racial discrimination, later broadened to general discrimination topics.
But that is just the US, and e.g. in Germany these roots (and also the connection to wake/asleep) are mostly missing.
So it is just a normal imported word, with no clear antonym existing.
Also because of this only recent import of the term, it is less connected to its original meaning, but often only associated with a well-intended, but superficial kind of activism.
E.g. it is heavily associated with a generally not very popular over-gendering going on in official and news texts, which leads to a broken kind of the German language. (German is heavily gendered, but a word’s gender often has nothing to do with the sexual gender).
So the term had a somewhat negative connotation to begin with, even in more progressive circles.
Doesn’t hinder the far right from doing anti-woke campaigns nonetheless, wokism is just such a nice (but actually in the broader population none-existent) opponent. And they use the term “Anti-Woke”, because it just makes sense for an imported word.