Or, the closest you can get to a nonbinary pet... These type of pets appear as FEMALE in the game, but can mate with both male and female pets! The only catch is they have to mate naturally, as you can't use PetzA to force them to mate. Nothing less, while this can occur as a glitch, maybe you wanna hex a specific pet into being a nonbinary (lesbian.) Let's start.
First, make sure you have A HEXING PROGRAM (I use ICY Hexplorer.) If you're not good with checksum (like me, and I'll use these in the tutorial,) download Python 3 and PetzByte!
It's also useful to change your pet into a male using PetzA, so that way you know it's nonbinary by it having a female symbol rather than the male one.
Open up your hexing program and search for the third instance of "p.f.magicpetzIII".
Without explaining too much, the 00 that's selected (the second byte) is what defines your pet's gender. 00 is male, and 01 is female. If you change it to anything else, they'll become NONBINARY. I'll change it to FF for simplicity. Save, and you're done with that!
Now, if it weren't for CHECKSUM being a thing, this would be over. However, NO! THAT'S NOT THE CASE!
If you haven't, download Python 3 and PetzByte as linked. Don't worry about the Python 3 file after you install it. Instead, put the PETZBYTE.PY file either on your desktop or in a folder you'll remember it in.
From here, simply drag your .pet file over the .py file.
The terminal should open up and say this (just with your pet's name and not Burger.) Press any button and then close it.
Now, when you go in the game, your pet should work!!!
Things to note though, when your nonby pet mates with another female, both pets will be pregnant. Sometimes the game can make an oopsie and you can adopt or breed a nonbinary pet without knowing, too.