At our house:
two piece=yes. I love rash guard shirts and boy shorts, or tankinis. Comfortable, functional, win all over.
triangle/string bikini=no. I think to myself - why do grown up women wear triangle bikinis? Not really primarily for comfort or function, you risk a wardrobe malfunction if you get too active. It's to look good, and look appealing. To look sexy. And there's nothing wrong with that if that's what you want to do as a grown person who is capable of being in sexual relationships. I don't want that to be a consideration for my kid until they are at an age where sexuality comes into play. That's my objection to "sexy" or "adult" clothes on little kids (well, little girls, let's be realistic). It has nothing to do with whatever pervy creep might be around gawking at my kid, cause she could be wearing overalls for all they care. It has to do with the mindset of why do you purchase a piece of clothing. Comfort and function come first, for a little kid. Fashion comes second. Looking hot comes a way distant third, when they are starting to contemplate sexual relationships.
Some may say I'm reading too much into clothing. I go on seasonal school clothes shopping rants about why little girl's shorts have a half inch inseams and are tight, and little boy's shorts have a 4- inch inseam and have room to move. Why little girls' jeans are skinny/boot cut/low rise, and little boys are relaxed fit/carpenter. Why little girls' bathing suits are minimally and strategically placed, and boy's board shorts are practically coulottes - ever seen a pair of Speedo swim briefs in a boy's section of a regular clothing store?
But maybe I think too much about it.