The joke is:
Non-binary refers to people not identifying with either being exclusive male nor female.

The post shows someone asking ChatGPT what this is called in spanish.
As spanish seems to have gender for nouns, this defeats the purpose of being neither female/male.

A non binary person would be "una persona non binaria", which is a gendered word, female.

It partially makes sense. Non-binary in Spanish is gendered depending on the subject. But it is not a real gender. Person is "female", human being is "male". But they are generic words

It's an adjective so it must match the gender of the noun before it. So if you want to say non-binary person, since person is femenine, you'd say "persona no binaria". Unfortunately, however, most nouns change gender depending on the gender of the person referred to. So you can't say non-binary gardener without resorting to "made up" grammar.

Imagine if you’d asked it for a vegetarian recipe and it asked if you wanted it to have a chicken or beef base. It’s sorta like that

The joke is that someone who is non-binary doesn't identify as male or female, yet Spanish is a gendered language and thus ChatGPT provides male and female forks of the word "non-binary".

In Spanish, everything is gendered, usually descenable by an -a or -o ending.

So Spanish requires you to pick the male/female linguistic gender to refer to a person in order to say that their gender doesn't fit on the male/female binary.

I believe Spanish speakers just resolve it by using -o by default, because linguistic gender is not identical to social gender.

It's roughly like if English made you say "they're masculine-non-binary".

As a Spanish speaker the joke does make sense as is referring to how Spanish is usually spoken but it misses the detail that there's now the use of new gendered words. Is really hard to explain in just a post but is a preview substantives in Spanish have a gender even things that you wouldn't consider gendered they have it it affects the use of the words and how you address people.
For example a simple word like "the" note that table is mesa and book es libro sona simple translation like The table >becomes> La mesa The book >becomes> El libro The translates to La or El depending of the "gender" of the word. Is not that we consider every book male and every table female but we use gendered pronouns for objects and there is gendered words for everything that refers to a person. For example nurse translates to Enfermero or Enfermera depending if you talk about a msle or female person respectively, note the word ends in o or a now the troubles are if you're using plurals it will be Enfermeros and Enfermeras and the first refers to a group of people that can be all male or mixed male and female but the second refers to a group of people that is only composed of females and worse of all nonbinary people are not comprehended into any of this. You see the language is always throwing everything into male female bins even unwillingly and for a non gender conforming person that's hell. Now we could fill a book with how we are handling it but it has been tried to use the letter e returning to the nurse examples it will be Enfermere but the particle now is Le Enfermere and Les Enfermeres and now the second would be totally gender neutral and refers to a group of nurse people no matter the sex. But there's a truckload more nuances. General neutral and how we use it is an ongoing problem in Spanish that we haven't fixed it yet, and there's no general concensus Of where is going.