Given a choice between wearing a bikini and a headscarf (of the religious sort), would anyone actually choose the latter voluntarily? It seems counter-intuitive to think so, but perhaps that's because we have certain cultural biases that value the freedom of wearing whatever we damn well please over the freedom to cover up our bodies and not call attention to ourselves.
Yes, they're both freedoms, but the sad thing is, it's a zero-sum game: we have to choose one freedom over the other; and regardless of which we choose, when we find ourselves running with a crowd of 'the other' we do call attention to ourselves like it or not. In that situation things can get uncomfortable, if not hostile.
The two choices of dress reflect two mutually exclusive philosophies regarding the self. The headscarf route is taking the comfort of anonymity, hiding oneself to look exactly like everyone else so that there can be no basis of comparison between one female individual and another. Regardless of what she looks like -- fat, skinny, flat-chested, pot-bellied, knockout gorgeous or hunchbacked -- everyone looks like a generic 9mm slug, and that's ok because no physical characteristic can possibly make her self-conscious or feel the need to do anything about it. Being comfortable with oneself, knowing there can be no pre-judgement from other people over the trivial matter of physical appearance is one of the best freedoms the world can afford.
Wearing a bikini represents the freedom to, um, I'm not really sure what. Bikinis show off things about oneself that we'd rather not show. We're constantly worried that we could come undone and reveal more than what we're prepared to reveal. What it does is that it places the responsibility of our presentability in public squarely on our own individual shoulders. To ensure the right things stick out and keep the wrong things tucked in requires Work. It means eating right (in most cases that's mistaken for eating less); it means a punishing exercise regimen to sculpt and maintain a shape that first satisfies the self (good luck with that) and then satisfies others. And yet, not be too satisfying to the wrong others to avoid attracting unwelcome attention. That's a lot of rules to follow, many of which lie in fuzzy grey areas, for what we consider our "freedom".
Me, I'm not really sympathetic to either camp. I myself have never lived in fear of a wardrobe malfunction; nor been a victim of lascivious staring; nor had any such related problem. Regardless of what I wear, I swear I'm quite invisible to the crowd. I imagine even if I wore my skimpiest speedos in public few would notice the pasty apparition ambulating in their midst -- except for a sensitive minority mainly comprising small children who would react in horror, recoil from the ghastly sight and maybe have nightmares for weeks after.
The happiest women, I think, are the ones who wear bikinis and can't be bothered about what anyone thinks of them. Think I saw some of those in Florida...
In case you're wondering, I'm just musing over "Bikini or headscarf -- which offers more freedom?"