Well, "woke" doesn't really mean anything. It's just a vague, nebulous term that's used to refer to anything that right-wingers don't like.
But I would argue that the majority of right-wingers can't be Trek fans without being hypocrites. Unless they only watch it for the cool spaceships and look no further, being bigoted and prejudiced goes against the entire message of Star Trek's nearly 60-year history. I see a lot of people on Twitter complaining that new Trek is "too woke", and I can't help but think that they really just don't understand old Trek if they think that it is in any way more compatible with their views than new Trek (unless they just watch "Code of Honor" and "Profit and Lace" on loop or something).
Well... yes and no.
Like, overtly,
Star Trek has always rejected racism and celebrated diversity.
But even setting aside whether or not
Star Trek usually lives up to its purported celebration of diversity -- and I'm not convinced it does...
The thing about
Star Trek is, I think it was Bryan Fuller who argued that liberals like
Star Trek because it's a future where everyone's equal and things like poverty, disease, war, racism, sexism, bigotry etc have all been overcome -- and conservatives like
Star Trek because it's in a setting that's intensely hierarchical, where everyone is a member of the same paramilitary organization, everyone's wearing the same uniform, and the paramilitary institution and its leadership is almost always wise and correct at the end of the day, where colonialism ("IN SPACE!") is benevolent, where violent resolution of conflict is framed by the narrative as acceptable, where telling foolish natives how to live their lives is the right thing to do, where the power of the state to expand is unquestioned, and where it's okay to engage in biological essentialism against aliens whose choices we don't like.
Star Trek, from a certain POV, is a fantasy of benevolent colonialism and expansionism, where characters can engage in biological essentialist stereotyping, starring space cops.
So... yeah, I do kind of understand why
Star Trek also attracts right-wing personality types. It's a franchise whose most essential thematic impulses are frankly in some tension with one-another.