All of this should be troubling to anyone actually concerned about women's rights. Typically, though, concerns are dismissed as Islamiphobia by feminists as part of the theory of Intersectionality.
Is she allowed to drive a car or even go out by herself? Is she allowed to handle the family money or does her husband own everything and keep her on a small allowance? Did she choose her husband for love or was he chosen for her? Is she at risk for female genital mutilation? These are not idle questions. I live two miles from a radical mosque (two of it's members have gone to fight with Isis). Female genital mutilation is becoming more common in the US. Estimates are that it's been done to thousands of women living here. Arraigned marriages are also fairly common with the groom traveling to his homeland to meet his bride for the first time just before the wedding.
In theory this is an individual choice but every time I see a woman in a headscarf (normally several times a day), I wonder about what other traditions the woman is being pressured to follow?
All of that changed with the rise of Islamic fundamentalism. Even in Western countries, there is pressure on women to follow "traditional" dress.
Similarly, when women from Muslim countries immigrated, they also assimilated and dressed like their Western neighbors.
I'll make a few other points to put all of this in context. The burkini is a very recent invention. It is part of a general trend among Muslims to control women. While wearing headscarfs is the norm in Muslim countries today and enforced by law in many of them, that was not the case a couple of generations ago. Women in Muslim countries in the 1960s and 70s generally didn't cover their hair. That was something their grandmothers did (the great-great grandmothers of today's generation).
Columnist Kathleen Parker wrote a column comparing the fight for Muslim women to cover themselves with the fight 100 years ago for Western women to bare themselves on the beach. This is another false equivalent since men were also fighting to show more skin 100 years ago. While concentrating on a patriarchal society telling women to uncover themselves, the burkini only exists because a patriarchal society demands that women hide themselves.
The burkini, in contrast, is worn instead of a western-style swimming suit. It has no utilitarian purpose. It is only worn by women and only because Muslim culture requires it.
Violence broke out recently in France after several seaside towns banned the burkini - a swimming suit for Muslim women that covers the entire body except for the face, hands and feet. I've seen various columns and memes on the subject. They tend to deal in false equivalences.A recent Facebook meme shows a woman in a burkini and a woman in a wet suit pointing out that only one is banned. This is a false equivalence for many reasons. The wet suit is used to protect a swimmer from cold water. It is not normally worn in a swimming pool or on a beach (unless the wearer is surfing in cold water). Men wear wetsuits at the same time, for the same reason as women. There is no cultural reason to wear one.