Hell, I'm not Muslim and I'd prefer something like this over a regular one-piece swimsuit. I'd never wear a bikini to begin with and I really don't like swimsuits in general. I'd heard about "burqinis" before but never really thought much about it.
It lead to reading about "modest swimwear" for Christians. Bleh. I don't wear skirts and dresses. And especially not in the loudest floral prints possible.
I was thinking that I liked the idea of modest swimwear, but I hated how it's exclusively associated with specific religions. I also wished the burqini didn't have a hood and the "modest swimwear" weren't as ugly.
Then, from Image Googling, I found women's long-sleeved rashguards for board surfing. They come in nice, sane colours and patterns.
Not that I want to go swimming often enough to warrant more serious thought on this, but maybe a somewhat loose-fitting rashguard with ¾ length yoga pants in the same material would work. I used to be a front desk attendant at the YMCA and I know there were issues with certain fabrics not being allowed in the pool. If I did want to wear that, I would phone the facilities ahead of time and ask first, but I can't see it being a problem.