In my experience most (not all, but most) women couldn't seem to give a hoot that a bearded bloke is scrubbing the toilet in the next cubicle while they are doing whatever they were doing in there
And, as I also clean the Men's toilets next door, I can, hand on my heart, say the women's toilets are always messier. But more paper on the floor and more wee too - I regularly have to mop women's cubicles but hardly ever the men's
Firstly, how would you know if women are bothered? If they are, they walk away when they saw the sign. If they can't wait so feel forced to use the toilet while you are there, most women are socialised not to confront male strangers - they are unlikely to tell you if they are bothered.
Secondly, it is hardly surprising that women's cubicles are messier, as they get far more use. Men can use urinals 90% of the time, and they are less likely to be accompanying small children to the loo. Women's cubicles probably get at least 10 times the use of the men's ones, quite a bit of it by young kids.
I have gone into women's toilets that are messy, but I have never gone into one and found piss all over the seat, the way I often do in toilets shared with men.