Captain Tracy ~ "Horrifically offensive?" I don't think so.
Star Trek was coping with the absolutely novel idea of women in the military. Not just feminism in general, but it placed women in military roles, command roles. This was a radical idea at the time, and you can see Star Trek grappling with the roles of women EVERYWHERE, especially in the first season.
First, it's the very awkward Pike line about Number One. Number One does a double take. First because Pike says he can’t get used to having a woman on the bridge, and second because he says “you’re different”. The implication of the discourse is that Number One cannot be both feminine and in a command role.
Then Gary Mitchell's crack about Dr Dehner being a "walking freezer unit". Meanwhile Gary Mitchell is hugging that female officer on the bridge as they're just about to get clobbered by the barrier. It was confusing and inappropriate -- affection is something you don't display in a military setting, because it impairs discipline. But in the pilot to the show, (Where No Man), they hadn't quite figured that out.
As with Charlie X and Mudd's Women, the writers couldn't decide whether women were a sexy foil for the stories or something else. They put in sexy Yeoman Rand and that wasn't right either -- she only lasted a few episodes. A female yeoman keeps interfering with the ability to write romantic relationships into the scripts, as we saw with "Dagger of the Mind" and Helen Noel.
Captain Tracy -- I'm responding primarily to your long post.
~ Mister Atoz
The one I hate the most is from "The Cage", when Pike, exasperated over his flustering yeoman, says "I can't get used to having a woman on the bridge..." then looks over at Number One, "You're different of course, Number One."
I understand the historical and cultural context, and GR might have even thought he was being progressive about pointing out the woman on the bridge...but in the 23rd century, that would be something new and remarkable? That just seems anachronistic even for 1964. And condescending. And it's not as though she was being incompetent, she was just...nervous, like any young officer on the bridge of a starship might be when it was clearly her first assignment. I don't know, it just always bugged me.