This one took a bit to figure out, and some NBT snooping was needed to find the cause.

Breeding two fish and incubating the eggs from two identical parents yields 4 different fish. All visible traits are identical, yet there are to different types of males, and two different types of females. After digging around in NTB playerdata for the fish item data, it turns out that there is a secondary gender, leading to 4 sexes:

Male - Male, Female - Female, Male - Female, Female - Male

Now, I'm aware of the whole "Gender fluid" culture, but did we have to get the fish involved?