The burkini is a great example Julie as as Erica says, it is not so much about hygiene. Hygiene is a good point but men can walk with their boardshorts outside and sit in the metro and you can't do anything about it.
Stricter rules are needed in order to keep the hygiene. Is this girl really planning on swimming in this swimsuit Erica? (Is it a swimsuit?) On the other hand a full length swimsuit is not a problem.
I remember seeing in a Parisian pool many years ago a beautiful women wearing a bathing suit which looked like a cocktail dress. Different from the burkini in that her top was free but most of her body was covered. It was still a very beautiful suit which I doubt anyone would complain about.
I think we have to admit that the issue here is not as much about hygiene but about our sensitivities. There is a reason people go to the pool, and to the
seashore, and freedom is part of it.
Suppose people would want to wear S&M gear to the pool, or even on the streets?
A woman wearing a mouth-gag, or a man would wear this:

(I'm not putting a picture of a woman wearing a mouth-gag as I find it too disgusting to want to see it here).
Certainly about the mouth gag you can't claim it should be banned because of hygiene but because it hurts our sensitivities. It's the same reason nudity is usually not allowed, and though I find it silly about nudity as I see nothing offensive about the nude body, I do see something offensive about women being subjugated. And whether they choose to wear the burkini, or are forced to, they are being subjugated.
Would you like to see women go to the pool chained?
The fact that this is supposedly a rule of a major religion doesn't seem to me to be an excuse, as yes, women were subjugated for many years. Besides, nuns don't wear the burkini.
I agree with Debby that they have the sea or private pools they can go to but this shouldn't be allowed in public pools.