Personally, I don't carry anything for water crossings. Like a lot of people on these forums, I hike in lightweight breathable trail runners. So when I come to a stream I just keep on walking. Lightweight mesh sneakers dry pretty fast.
As for barefoot or socks… it depends on the waterway of course… but in general, I don't recommend crossing in socks or barefoot. Too dangerous. But if would vary depending on the creek / river.
As for surf booties… I own a couple of pair… some XCEL 4mm for winter surfing and some ONeill 3mm for spring / fall surfing. Neither of them have any tread or support of any kind really (the would be the soft sole variety mentioned above). I would say again that these might be dangerous for water crossings. Their sole purpose is to keep your feet warm. They're not designed for walking.
Personally… when I'm crossing a fast moving river I like to have proper footwear on my feet (as opposed to Crocs or barefoot). I have not seen the scuba style boots mentioned by the previous poster.
BTW… there are also what surfers call "reef boots". They are designed just to protect your feet from… well… a reef! They're not designed for warmth. So they are usually a lot smaller (i.e… low cut) and lighter. Still no real tread or support though.
