You prefer to make an error, even when informed of it? You are an anarchist.
I like all the alternatives given in links in this thread more than the suit in the OP. I can’t put my finger on why I don’t like it. I don’t think it’s the Muslim thing. I just don’t think it looks very stylish for some reason. I think it’s the length of the skirt or something. It’s not asymmetrical enough. It cuts off at the wrong height.
Man, I would be so mad if they put one of these over the pool where I live. Part of enjoying the pool is enjoying the sunshine, dangit!
(Feel free to quote this page in a few years when I get skin cancer).
If I saw you in a burkini, I would assume you were muslim, perhaps because I’m used to seeing white muslim women (generally converts who have married a muslim man). But then I live in a very multicultural city, it might be different where you are.
I think the stingray stuff looks really great - I much prefer the sporty look than some of the other modesty stuff. Sporty looks cool and appropriate for watersports, the other stuff looks middle aged and square.
I like some of those. Some of them kind of look like PJs though. I think I’ll peruse a few of these sites again and go swimsuit shopping. 
That just sounds really uncomfortable to me. Swimming and splashing around in the pool are fun physical activities, and I would have a really unpleasant time if I were being squished by tight clothing aimed at condensing my body into a smaller form. Spanx feels uncomfortable at the best of times, but even when swimming?
Okay, now THAT’S what I’m talkin’ about!
If I needed to assemble a modest sun-protective outfit, I would get the following:
Swim tights(or capris) with a wrap cover-up skirt in the floral pattern and the crew-neck long sleeve swim shirt in white. I’d wear a tankini top under the swim shirt for coverage and so that I could take the top off if I was in the shade or indoors. I’d ditch the skirt if I were actually going in the water.
Those are cute too. And most of the suits don’t come with hoods. You have to buy them separately.
Forgot to say–I love the ones on Simply Modest. They’re absolutely adorable.
I can’t remember the last time I went swimming and didn’t see at least one person in long sleeves and pants. Quite a few “burqinis” as well. I think of them as Swim Burqas and they are quite normal here.
For me, I just wear a higher neckline and a slightly longer skirt ( I ordered from Here: http://www.decentexposures.com/ and asked them to make the skirt about 5" longer.
I suppose every pool probably also contains one or two people who are shocked and appalled by anything out of the ordinary, but really, you can’t satisfy those people anyway. It’s best to decide early on not to care what they think.
Some more links for the OP to look at:
Aqua Modesta–but these look so normal that the odd looks might come after you don’t take off your “coverup” to go swimming but just go right in wearing your dress. They’re also just made out of normal swimsuit fabric and not spf fabric.
Primomoda, like the style in the op but more swimsuity colors and design details.
As far as reactions go, if I saw you around the pool in one of these I would wonder whether you were sun sensitive, religious, or just plain modest. I don’t think I’d bother asking though as none of those options makes for very interesting conversation. 
You might get asked, but I think as another poster put it “I don’t want to get skin cancer AGAIN” or “I don’t want any MORE skin cancer” is a succinct enough way to satisfy their curiosity, and as it’s the truth besides, a very simple thing. Of course, that might open you up to hearing people’s wingnutty theories/stories about cancer. But those are the crazy people who will talk your ear off about anything anyway.
I’ve worn bike shorts under my swimsuit for a decade now, and I’ve had one comment on it - someone asked me if there was a yoga class starting. I don’t know what people assume, and I don’t care - I’m more comfortable when I’m showing as much skin as I’m happy showing.
How about a Dive skin? These are very thin and lightweight and will give you adequate UV protection while also being more western in design. I’d immediately assume you were muslim in the burquini.
I really like these. Thanks for the links.
Some of the other sites listed don’t have things in my size. It looks like they do, but according to the size charts, they don’t. Their 20 is really a 16.
I don’t like anything I’ve seen so far on the simplymodest site. I want coverage to the wrists and to the feet. I appreciate the suggestions of a short sleeve shirt and swim skirt, but it’s not near enough protection. I’m not worried about modesty, I’m concerned with sun damage. I just want something that will look OK on my size body.
Thanks again for the links. There are better options than the suit I linked to in my OP. I just have to find something that works for me.
Notice the lack of fat people in those photos? Yeah, you wouldn’t want to see me in one of those. :o 
HydroChic- it looks like you can buy “swimming pants” and 3/4 length sleeves as separate parts. They also have plus sizes.
If you’re looking for other things to search for, try Orthodox Jewish sites. Search “frum swimsuit” or “tznius bathing suit” or something along those lines.
Well maybe it wouldn’t look awesome, but they DO come in plus sizes and are easy to get in and out of. They are also lightweight and won’t make you hot or sweaty when you aren’t in the water.
Indoor pool.
I realize that wasn’t the question. But, it is the correct answer if you have had health scares due to the sun.