I'm way overthinking this, but I'm going with finite. It could be an unfathomably large number, but gender is a human construct and there are a finite number of humans. Let's say each human that ever lives has a unique gender identity - there could be billions or trillions, but it would still be finite.

this poll is homophobic, gays are not good enough at math to know the difference between countably and uncountably infinite /s

Does the set of all genders contain itself?

Countable infinite. Infinite because there are infinite possibilities. (Spectrum) Countable because the number of human beings is countable.

A finite number of genders will be experienced by people, but there are an uncountably infinite number of genders.

The set of genders is like the real number line. You can throw a dart at it and pick out a new gender for every person, but you will never be able to throw enough darts to exhaust the set, even given infinite time.

With enough funding, I will finish my research on the Hilbert space of genders where every particle in every possible reality has a one-to-one correspondence to a gender. I call it the "Everettian gender hypercontinuum".

I just respect everyone and never assume their identity is what I initially (subconsciously?) think. It took a long time to get there, but I just take every person as a person worthy of respect and dignity as my default.

I guess it depends on whether we’re willing to say a gender exists if theoretically possible though not ever embodied. Will artificial sapients have gender identities?

I'd say finite, up to 8.1 billion options. My throught process is that what isn't alive doesn't count.

"decides"

How arrogant are you? You don't get to decide shit.

I'm glad to know that I've reached peak beehaw today.

That's a hell of a question, buddy