So for us regular folk, being woke, basically means you have your head up your ass.
No? I'm still not sure where this misunderstanding is coming from.
The OP story is definitely a clickbait sort of premise... and wants to say that women find liberal men (feminists) less attractive than alt-right/modern right leaning men (woke movement).
People are supposed to be on the "woke" side of this comparison.
The term "woke" has been co-opted a little, but not enough to cause this much of a mix-up in definition. Someone that considers themselves "woke" tends to be more skeptical of government/news narratives, seeking the actual goings-on behind what they're being told. It really has nothing to do with sexuality or manliness.