It looks bad if she cares about height if you just flat up ask her, alone, without peers.
It does not look as bad if she admits to it with and to her peers. You get to see mate pre-selection in action! There's a lot of chiming in. This is where the performative disdain appears. Disdain, because you will see expressions and utterances of distaste or even disgust; performative, because she is communicating this preference with her peers, partially for validation. You can catch women and even girls doing this. There's a hint of social jockeying in there. After all, by rejecting (or even pre-rejecting) someone, you're ranking them lower than you in some fashion. And there's really only two ways to increase your relative status: bring yourself up or tear someone else is down. Which is easier?
It also doesn't look that bad if the height question is mixed in with tons of other questions, and she isn't looking anyone in the eye when answering. This is the private milieu. Here, it's a questionnaire. She's at least taking a swing at being honest with her preferences.
Well, it's been a few decades, so my memory is limited. "Attractiveness" was a general self-reported category and women rated themselves higher. Interestingly, attractiveness and height overruled religion for women, even those who reported the religion answer as being at the highest rating on the scale.
We did have some psych tests besides the "barely above astrology" MBTI, namely the Taylor-Johnson.
I don't think you're going to see a lot of hardcore studies. Even OKCupid redacted their conclusions. It's really one of those areas where average people aren't ready to hear the results. The results would be unpleasant for the tabula rasa crowd and their buddies, the people who are against gender essentialism. And if it might present women in a less than brilliant light, consider the "Women Are Wonderful" effect.