How many genders are there?

[Klobmentum Mutilated Herself]

Joe Biden's hilarious answer to this, "there are at least three", was unironically a fairly good answer. I say that because the quantity of genders doesn't really matter much, gender can mean a lot of things to different people and it doesn't really help anyone's relationship to their gender or lack thereof to try putting a number on it.

For all practical purposes, there are men, women, and nonbinary people.

What people who troll in bad faith about "400 genders" and "blorp/blorpem" pronouns don't realize is that while, yes, there a lot of different specific gender identities besides those three that are confusing to cis people — your genderfluid people, agender, bigender, demigirls/demiboys, etc. — and those gender identities and expressions are all valid, but those fall under the umbrella of nonbinary, and people with those nonbinary genders are almost always content to identify themselves as nonbinary in cis spaces. The deep gender stuff and neopronouns are usually aimed at a queer audience, not a cis one — this goes for neopronouns too; many people who use neopronouns are fine with using they/them in cis spaces. Nonbinary (and its synonym, genderqueer) is a catch-all term for anyone outside of the man-woman binary, not a description of a one specific form of gender expression.

So there are more than three genders, but there are no fewer than three or four (some intersex people identify with intersex as their gender in addition to their sex, while many other intersex people identify inside the gender trinary of men, women, and nonbinary — also, many of them are trans). A precise number doesn't matter because there isn't necessarily one to begin with, but for categorization purposes, almost everyone will fit under one of those three or four big tents.

My answer in a queer space would be different and less pragmatic.