I was just combing the adoption center, and stumbled across Tneshi, a gender-neutral pet.

How is this possible, exactly?

either with a genderless berry,

or by adopting a cadogre or endeavor from the adoption center on Atebus. c:

Cadogres and Endeavors, being robots, are genderless by default if you create one. Then you can change that pet to another species but keep its gender-neutral status. There's also the which will turn your pet genderless.

Thanks :] I rather like the idea of this genderless...ness :]

and steamwork pets are technically genderless when "manufactured" as well.

Steamworks pets are mechagendered. :)