I am a full-scale life-long Trekkie, so I can confirm this. Original Star Trek was very woke, for its day - in some ways. Mostly it was very good on the racial front. It had a Russian bridge officer during the height of the Cold War. It had a Japanese bridge officer when most Americans still had WW2 fresh in their minds. It had a black officers during the tensest part of the civil rights fight - not just Lt. Uhura on the bridge, but guest stars as Starfleet medical doctors, distinguished Federation scientists and diplomats, and other "good guy" characters. That first-televised-interracial kiss kind-of happened - it happened on set, but the camera angle hid the lip contact. Still a good step though.

Now there's a giant asterisk to all this: original Star Trek was often incredibly sexist. And I don't just mean in terms of wardrobe for women guest stars. For example, it's mentioned in several episodes that there were no women commanding starships in Starfleet, and this was treated as "normal". The final episode involves a bodyswap between Captain Kirk and a woman who was denied a captaincy in Starfleet, and Shatner-as-her plays her as the most awful stereotype of a histrionic irrational woman you can imagine. Uhura's actress was treated poorly by the writing room as the series went on and she got less and less screen time. Women regular and guest stars were not often treated as real people, but as sex objects to simp all over male Starfleet officers.

Edit: I forgive and accept simping on Spock, either in-universe or in fandom. That combination of physical, emotional, and intellectual power barely contained by sheer force of will is just magnetic. You desperately want to be the one to make them smirk or get flustered or get tongue-tied in your presence. Vulcans are incredibly sexy.