plenty of animals can gender swap, be hermaphrodites, or produce asexually.

I don't entirely agree, because gender identity is known to be at least partially biological, e.g. there are correlations between transgenderism, skin elasticity, and hyper-flexibility.

Adding to this: XX and XY works for mammals, but not for other vertebrates (fish, birds, reptiles, amphibians). Birds and reptiles have Z and W chromosomes, and unlike in mammals where females are homozygotes, males in these groups are homozygotes. Some reptiles have temperature dependent sex determination, where ambient temperature above some value will produce males or females (depends on species). Some reptiles are composed entirely of females.

Some fish will straight up change sexes depending on age and male-female ratio in a social group.

In other groups it's not even different chromosomes but simply copy number of specific genes.

Plants can do all sorts of whacky things like produce seeds and pollen in the same individual.

Fungi are an entirely different cluster fuck because they have mating types which are not simple binaries.

Eukaryotic sex determination isn't a binary and it isn't even a nicely categorizable spectrum. It's a grab-bag of whatever doesn't perma-fuck your genome.

Source: me, I'm a biologist. Though admittedly I work on animals so my understanding of fungi and plant stuff is fuzzy at best.

https://xkcd.com/435/

I would say gender is probably centered about around psychology, ranges mostly from sociology to biology, with a just little bit going into chemistry

maybe like

Slime mold(which is not a mold or fungi) looks around nervously in it's 13 different sexes.

What kind of fungi should I consider for the maximum giggles?

Psychology is technically a branch of advanced biology