Supply and demand drives culture, but it's kind of a feedback loop. Artificially lower the demand for women and raise it for men, behaviors will shift accordingly. I don't necessarily agree with every hypothetical put forward in this thread, but there are some good observations here. I think there are some factors of gender relations in our culture that are not inherently tied to the supply and demand. For example, I'm not so certain that aesthetic care necessarily changes; humans are a rare species where the female preens more than the male, but realistically, it makes more sense that the person in more demand preens less. I'm also not entirely convinced that all factors of society flip on a 1:1 basis. I don't foresee the supply and demand element changing the existing power dynamic by itself; men are still innately bigger, stronger, more aggressive, and think differently. On top of that, women have to deal with 9 months of pregnancy and have a harder time proliferating since they can only carry so many children at once whereas men are theoretically limitless. Ceteris paribus, I would more bank on something like virginity being seen as a form of machismo. That said, in this scenario, women absolutely become a lot more sexually assertive and probably a good deal more vulgar; desperation versus standards also flips upside down. Views on sexual performance might also change in interesting ways. Penis size would probably be a lot more 'forgivable' (in line with vaginal width in our society, I suppose?), premature ejaculation from a guy would probably be a sign of female excellence, erectile dysfunction would be seen as a major failure for the woman, being unable to orgasm would probably be seen like our society sees erectile dysfunction. Definitely much more women-centered porn and male body objectification in fiction. Dick pics become all the rage, tit pics become the new dick pics. Oddly enough, blow jobs probably become *more* common (although not until climax) in order to get it ready to penetrate. Cunnilingus also happens more because it becomes a way of getting the woman off without having to have sex.
Now, something I would be interested to consider is the *how* of either something like this or if we wanted to create a society more likely to reflect some of the things mentioned above. In that case, there's a few ways we can go about that. The easiest IMO is to drastically shift the gender ratio of the population. A lot fewer men would drive up the demand of men exponentially, and would also give women a lot more room for systemic power. The potential consequence of that is normalization of harems or concentrating power in fewer men in order to consolidate resources. That all really depends on how women choose to handle the situation though, so that could be written to go either way. One way that could be handled is by having males be drastically reduced as a percentage for a few generations, but gradually shift back to equilibrium after some time. That would give some time for the demand for men to spike and for women to take the reins of society, but then bring the ratio back to baseline enough that harems aren't the norm. A backlash to a harem-based society could then result in the type of scenario where men are sluts and women are studs.
I also considered that a higher percentage of men could also potentially shift things, but I think in that situation, war just becomes more common and power more concentrated -- so, basically imagine current society on steroids.
Another possibility to accomplish this (with results much more in line with the 1:1 flip that people seem to want to see) is by changing some of the power dynamics. So, keep things relatively the same for men -- but now all women are Amazons (or some kind of monster girl that is innately stronger than human men). That would greatly flip the roles in a systemic sense. Alternatively, if women could be much more intelligent and thus more able to accumulate wealth and exploit the physical labor of men to maintain a female hegemony. Another possibility is that these changes happened early on enough in human society that humans have evolved in ways to reflect the changes (ie: more biological aggression among women, passivity among men, refractory periods flipped, physically stronger women, possibly even shorter gestation time, etc).
It would make an interesting world to explore at any rate. I actually did an RP with someone where we used some of these concepts and MC was a male escort with no other career opportunities. Made for an interesting story.