Privilege blindness doesn't just apply to straight white men. The relationship status of the people has nothing to do with it. Men are instinctively predisposed to helping women. Women can and do take advantage of this, and generally don't recognize or acknowledge that they are doing so. You don't see it, because you've lived it your entire life and it is normal.
How many times has a woman put a new water bottle in the water cooler here? I know the exact number, because it is zero. All of the women here are fully capable of doing it, yet they ask men to do it. And how often do men say no? This is very obvious when looking at tasks that are considered stereotypically "men's work" like lifting something, but it applies just as much to anything else.
I've watched my wife get men to do her work for her several times. She simply asks them to do it, and they say yes. When I point it out to her, she insists that they would have done the same for a man, and that had she asked a woman they would have done it for her too. Yet, she never asks another woman to do it, and I know I sure wouldn't do it if a man were asking me. She is taking advantage of being female, and it is so deeply ingrained that it comes naturally and she doesn't recognize that she's doing it.