(The actual wording in the survey is: “Which one of these women is dressed most appropriately for public places?”
Maybe these results aren’t what they’re cracked up to be. After all, “appropriate” is a pretty ambiguous word, because it can refer to something that’s demanded by one’s social environment, or it can mean “that which an individual considers suitable and proper for herself.”
If I visit a mosque, I will take off my shoes before entering. The Muslims who worship there expect me to, and there is no point in antagonizing them over something so inconsequential. Removing my shoes, then, is appropriate within that context. But if no one was looking and no one cared, I would explore the mosque fully shod, just as I would a church — or a Walmart. In those environments, shoes are perfectly “appropriate.”
Likewise, a woman in Tehran or Islamabad might consider her uncovered tresses a perfectly appropriate appearance for her, and yet, mindful of social and religious mores, grudgingly choose to wear a chador or a head scarf.
And, as one commenter points out,
Since women can be arrested and prosecuted for not wearing the niqab in Saudi Arabia, of course the respondents would choose the garment that is mandated by the government. It has nothing to do with what they would choose for themselves [or] their wives.
Pew says that
Only in Turkey and Lebanon do more than one-in-four think it is appropriate for a woman to not cover her head at all in public.
This confirms the problem with the question — because when you ask it differently, you get very different results:
Saudis appear to be particularly conflicted, with 74 percent saying it is only appropriate for a woman out in public to dress herself in a tent (a burqa or niqab); at the same time, almost half of Saudi respondents — close to the number for the officially secular Turks! — believe a woman should dress how she wants.