Interpretation can be subjective. Carol could've done a naked fan dance and if it was done well, I wouldn't have found it offensive. It's not about the skin that was shown, but the tone of the scene.
It's a different issue, but I was skeeved out by the learning that Kirk had a one night stand with Chapel that he didn't even remember which led her to leave the ship. I don't have a problem with Kirk being promiscuous, but it doesn't make him seem like a good captain if he's having one night stands with his crew so often that he can't even keep up with which crew members he's slept with.
That probably bothers me more because I am a fan of Chapel in TOS, and she seems like a very reserved, sensitive woman who wouldn't sleep around. I realize that's open to some interpretation, but what we see of her on screen is a woman who is grieved at losing her fiancee, and is pained by a long time unrequited love, so I probably would feel more protective over Chapel than if Carol had just mentioned a friend who'd slept with Kirk that we had never heard of.
I want to add that I like Pine's Kirk a lot, but I think it's worth discussing his short comings. TOS Kirk certainly got around, but I think he still had more sensitivity with how he treated women.