I've been thinking about this question for a couple of days and finally have something to contribute.
One of Betty Friedan's main arguments in The Feminine Mystyque was about how women's consumerism leads to inequality. It's been about 10 years since I read the book, but if memory serves, the "mystique" was the idea that there was one ideal of womanhood and it involved a lot of buying stuff, and also that it was conveyed to women through advertisements. (that were for the most part created by men)
Although male-targeted advertising is definitely rising, It seems obvious to me, that most ads are still directed at women. Women are still receiving more messages than men that being happy or even normal is contingent on the stuff you buy - makeup, clothes, home decor, a certain lifestyle that requires a certain amount and style of possessions.
One of the tenets of mustachianism is that we already have enough (see yesterday's post on the soldier of luxury). Although not being a cosumer sukka is good for everyone, it's maybe more important for women who are more fiercely targeted by marketing. In that way it definitely points toward equality.