If you went up to them on the street and asked, "Hey, how important is it that a guy be tall?" you would get a response that would sound a lot better than what they fill out with nobody looking. You have to take it out of a public context and also bury it along with a bunch of other things to de-emphasize it. Meanwhile, at one point Tumblr, Twitter had a run of women pulling faces of disappointment and/or disgust with the caption "When his height starts with a 5." And that's an in-group thing, neither private nor public.
People have a lot of different facets of themselves -- something that Zuckerberg really didn't get -- each shown to a different audience. If you've ever watched a bunch of women do this "performative disdain" routine, wherein they make displays to other women that they, too, have high standards, that's definitely a facet that is neither entirely public nor completely private. I recall a recent car commercial to that effect, where women were inferring something about a man due to his choice of vehicle, and were doing performative disdain based on that.