In the very first episode of Star Trek: the original series, we see a white Captain reporting to his black Admiral boss, a black woman on the bridge just a couple years after Jim Crow was abolished, wearing a short skirt (a symbol of feminist liberation at the time), a Japanese helmsman on the bridge only 20 years after the internment camps, a Russian crewmate on the bridge during the Cold War [edit: actually did not appear until Season 2 but the point stands], and the foundation of the modern concept of queercoding.
In the very first episode of Star Trek: The Next Generation, we see male crossdressing crew members, a female officer on the bridge in charge of security, a literal ship's counselor stationed at all times on the bridge, a single mom raising her teenage son on her own while juggling a full career in medicine, a blind mechanic whose "disability" is shown to be a strength, and an angry, all-powerful godlike being who is revealed to be simply a petulant child masquerading as a deity.
In the very first episode of Star Trek: Deep Space 9, we see a black man gain a powerful command position, respect the hell out of the customs of a religion he didn't understand, show respect and equal treatment to members of three other alien races he didn't understand, appoint a female guerilla fighter who defeated imperialist fascists to a position of authority within his administration and defer to her judgement in areas of her expertise, accept his friend's gender change, and tell his son he loves him.
Star Trek has always been woke. You just grew up to be a bad person.
I think the better question is "when did Star Trek start preferring awkward, hamfisted, and cynically inauthentic writing that makes you feel like you're watching community theater?"
The answer is a toss-up between partway through Voyager and Enterprise, but ENT was definitely the point at which Star Trek was no longer being used to speculate about the possibilities of exploration and discovery in an optimistic future, and instead became an embarrassing soapbox on the part of writers and producers who haven't had an idea challenged since they were in preschool. The entire 9/11 + War on Terror allegory is very possibly the most cringeworthy Star Trek content ever televised. That's really saying something considering we also have Discovery, an exercise in why you can't hire a bunch of hacks who all want to be Joss Whedon, nor give them free rein to produce a version of Star Trek in which every character is a creepy asshole who never shuts up and uses the kind of corny faux slang that only exists in TV commercials.
As with many things, I blame Rick Berman.