Actually, she says "Your world of starship captains doesn't admit women."Lester clearly states the Starfleet doesn't "admit" women, which would suggest she means in a professional sense, not personal.
Exactly. Look at her very specific choice of words: YOUR world. Kirk's world. His own, personal world. He can't have a lasting relationship with ANY woman. That's what she meant.
I mean, it's not as if the perfect utopia Gene Roddenberry was trying to create would be so sexist as to not allow female captains, would it?