Missed this a few days ago, sorry! But I have to disagree.
Look at all that again. And ask yourself: what was the purpose of this character? How were they treated on the show? What point was being made with the inclusion of this scene?
Because I'd say the character was introduced in a neutral to sympathetic way. The message being "this is just who they are". The child isn't unhappy or confused, it's everyone else who has the problem! As for the betting app, as you point out, it's portrayed in-show as a negative thing. The kids use it to fixate on ridiculous things and ruin people's lives.
I find it really hard to believe the message Matt and Trey were trying to convey with this one wasn't: "Non-binary kids are heckin valid and just want to live their lives! Their gender doesn't matter to anyone and wondering about it or trying to find it out is an invasive, childish thing to do!"
The message seems to be that the child in question is happy as they are and the kids (and by extension, the audience) don't need to know if their classmate is a boy or a girl. Matt and Trey never answer the question, and seem to withhold the answer as a kind of gotcha to the audience. The kids don't mock this new peer, as they once would have. And the show doesn't comment on the reasoning behind the character's strange decision to go through life hiding such a basic fact. We aren't shown any parents driving their behaviour, or given any other indication of what's going on here. Let alone a critique of the phenomenon.
My feeling is that South Park has sold out on this one. I agree they didn't go all in, but there was a distinct whiff of "protect trans kids" / "it's no big deal" / "my gender is none of your business" propaganda about this scene. It felt off.