It's incredibly antiquated to think that "left-leaning" means "hippies, druggies, and subversives." That's how many people in power in the '60s caricatured and lied about what liberalism is, to divert from the fact that it's really about civil rights, favoring constructive policies over destructive or regressive ones, and a standard of justice that applies equally to everyone instead of the privileged race, gender, or class.
Just saying that a starship's mission was to explore rather than exploit, to seek out new civilizations rather than conquer them, and to serve discovery over profit and power was an extremely left-leaning message for its day. TOS's generally anti-war, pro-peacemaking stance was very liberal, even subversive during the Vietnam Era. Including women and nonwhite people as equals in the service, and even a Soviet citizen (presumptively, since Leningrad was still named that), was extremely progressive and ahead of its time.
Although it was by no means atypical for 1960s-80s TV to be progressive and egalitarian in its messaging. The Twilight Zone frequently did allegories condemning war, bigotry, and fascism. M*A*S*H was certainly famous for its liberalism (an ironic contrast to the hardcore conservatism of the original novel's author), and there were shows like Quincy, M.E. and MacGyver that frequently embraced socially activist themes like civil rights, environmentalism, fighting corporate abuse, etc. Although there were occasional shows that seemed to take a more conservative stance, like Battlestar Galactica (which treated any character who favored peacemaking with an enemy as a fool or a quisling), although even it was progressive in certain ways (like not oversexualizing its female characters with skimpy costuming like most of its contemporaries did, while frequently putting the men in skimpy outfits).