Just purchased some Dyneema Socks (Barefoot Company) for kayaking.
These are relatively thick Dyneema based toe socks. They also have rather hard (it is described as rubber but feels more plasticy) grips on the sole. It is claimed that the Dyneema will prevent cuts to the feet - i problem I suspect we have all had time-to-time landing on some rocky or corally coastlines.
I actually have two aims from the socks - one is as protective footwear to avoid those cuts. Second is as part of my stinger gear so that if I do end up in the water in summer I don't suffer from a Box Jellyfish wrapped around my feet .
I have tried neoprene type booties/ shoes years ago. I found them too hot and also too sticky against the inside of the hull (i couldn't adjust my foot positions fast enough in dynamic conditions). I have used both normal synthetic socks (they just flop too much when really wet) and Injinji synthetic toe socks for the stinger protection (neither do anything for cuts). The Injinji's are perfect (most comfortable in the boat) other than the cuts issue and that they wear out in no time walking up a rocky shore. The Injinji's are also the easiest to swim with (feels most natural) of all the aforementioned options .
First impression of the Barefoot Company socks (not used in anger yet) is they are fairly thick, but the material doesn't seem like it will absorb much moisture. My large pair weigh in at 95g dry. The grip is very grippy, even on my wood and tile floors. Out of the bag they don't look well fitted but on the foot they are fine. The toes are longer than the Injini's and I don't completely fill them but the extra length makes them easy to get off. Key test will be their durability (they are reasonably exy) and how well they actually protect against oysters and coral (available reviews seem good). Based on my experience with Injinji's I expect they will otherwise be excellent in the kayak and in the water.
Not sure what others do for footwear but here is yet another option.