debatable. DNA recombination is only possible between two cells, but they do not have to be of only two different types.
Ant colonies have Drones, Workers and Queens. That are three genders.
Snails only have one Gender.
Humans have two. Everything else is a mutation, that not only has disadvantages. If your babysitter is gay, you could also call them a "worker". Wow, i like that statement, give me more inspiration! :D
Well, that's why I said (mostly).
There are not 1000s of genders. That concept is ridiculous, and a fiction invented by people who are either delusional or are making up nonsense so they can feel more unique and claim minority status.
I'm exaggerating, but the words' meanings:
gender: "Identification as male/masculine, female/feminine or something else, and association with a (social) role or set of behavioral and cultural traits, clothing, etc typically associated with one sex."
sex: "A category into which sexually-reproducing organisms are divided on the basis of their reproductive roles in their species."
Not enough folk realise this difference - gender is what you think, sex is what you are.