I apologize for the great ramble I am about to subject you to.
This is introduced in a notoriously bad way in the least liked season of the Legend of Korra, but there IS a spirit called Vaatu that sort of maps onto Bill's role. Vaatu is the spirit of darkness and chaos, locked in constant combat with Raava (aka the Avatar spirit). Vaatu and Raava got into a few particularly big spats that had massive implications for the world-- the first was that time they broke the barrier between the mortal and spirit realm, then there were two harmonic convergence events where Vaatu tried to spread anger and darkness to subjugate Raava once and for all. The first harmonic convergence event had the two realms walled off permanently; the second opened them both back up.
But the relevant part for Bill is that Vaatu is a trickster-- he played on Wan's compassion to get the upper hand on Raava, and also manipulated Korra into doing what was necessary to free him. Also Vaatu (sorta) had somebody who called him Muse-- a guy named Unalaq who was dead-set on freeing him because evil world domination I guess and becoming the Dark Avatar (yes that's really what it's called. The worst season of LoK, everybody!)!
That would be some delicious irony-- Ford's thinking he's being set up to be the hero when Bill is actually trying to make him into Unalaq. Instead of an era of darkness it would be Weirdmageddon, obviously. The Axolotl would take the place of Raava. The portal is a path to the spirit world, more specifically intended to lead to where Bill was sealed after the defeat of Unalaq. It's not an ideal time for Bill, who is extremely weak after getting his and Unalaq's butt kicked by DBZ Korra. But if he's able to get out, set up his own Avatar right this time, and get territory on Earth, he can greatly accelerate his self-healing and building up of power, allowing him to assure his own victory in the next fight against the Axolotl. Bill tries to compare his relationship with the Axolotl to Tui and La to get Ford's sympathy, saying that he got manipulated by Unalaq to justify what happened with Korra. It doesn't help that this is, on some level, reflective of how the Axolotl feels about Bill. Though the Axolotl does recognize Bill as invasive (Unlike Vaatu, Bill really isn't of this world or of any relation to what's within it), there is truly nothing personal or hateful on the Axolotl's end. Axolotl just likes balance and stuff, and he's fighting to integrate Bill into the harmony of the world. Axolotl wants Bill to be the push to his pull. Unlike Bill who is salty as hell and hates the idea of being integrated (due to his past trauma and desire to be cruel).
I like the idea that adjusted versions of the events of AtLA and LoK did happen. Meiji Restoration happens early somehow or Japan just never retreats into isolationism at all. Either way Japan decided to pursue becoming a major longstanding colonial power on par with the British Empire instead of pulling inwards, meaning that imperialist Japan happens way earlier and lasts way longer compared to our world and calls itself the Fire Nation because AtLA and it is majority fire-benders. Events of AtLA happens in the late-1800s with the events localized to the inspiring countries (Siberia/Northwestern Canada for the Water tribesmen, China for the Earth Kingdom, Japan for the Fire Nation, etc.) rather than around the world. Instead of the Fire Nation massacring all airbenders worldwide, they slaughtered the Tibetan airbending population, when Tibet had the largest concentration of airbenders in the world, as the capstone of a broader campaign to conquer Southeastern Asia and get a foothold to start chipping land off the Earth Kingdom. So Aang is still the sole survivor of a massive genocide, it's simply scaled to account for our world being way larger with more geopolitical players than AtLA's. Events of LoK happen around the early/mid-1900s and Korra is presumed by most of the world to have been killed during the fight with the Zaheer (the one where he purposefully triggered Avatar mode so he could kill her with it active and break the cycle), which was the same day the Stan bros were born. It's a coincidence (a lot of people are born every day) but Bill uses this to his advantage. Actually Korra didn't die there, but given her numerous mental health problems and the risk of being targeted again (bigger world = more extremists beefing with the Avatar) her friends and family agreed to keep quiet about her survival. Her actual death is in her sleep on the same day Soos is born. Again, a lot of people are born every day, so even after learning the truth Soos doesn't connect the dots.
I actually like the idea of Dipper being a non-bender. It would give him better grounds to bond with Ford and have the whole "isn't it stifling" thing take on a whole new layer of meaning (what with having to watch Mabel get noticed for stuff Dipper could never even hope to attempt). A big part of the internship is that Dipper wants to train with Ford, as he's got something of an affinity for chi-blocking thanks to his observational skills and small stature, and wants to learn more about it. He still ultimately rejects it, though it's a tougher decision he ultimately decides that he needs to grow up and have a childhood before dedicating himself totally to training.
Mabel on the other hand is a firebender and quite a good one at that, but her focus on combustion bending (which is notoriously difficult) makes her seem less competent than she actually is. It's actually an impressive feat that she's not blowing herself up or blowing off limbs regularly but that's hard to appreciate when you're having to put out small fires and repair objects somewhat regularly because Mabel decided to express her excitement with fireworks. All of Mabel's sweaters are at minimum slightly singed.
I do want to point out that bending affinities are a mix of heritage, interactions with spirits, and personality. Which element you get is mainly dependent on heritage. If your mom and dad are Earthbenders, or your parents are nonbenders from an Earthbending or Firebending line, you can't be an airbender. You could theoretically acquire airbending via training with the right spirits, or a Harmonic Convergence event where Raava and Vaatu duke it out for the fate of the world. But the former almost never happens since spirits are extremely fickle, and latter just straight up only happens every 10,000 years because all the planets align in a very specific way. This was a big part of why the Air Nomad genocide was such a severely damaging event. Once all the main family lines are wiped out, humans cannot (barring some spirit thing which is, again, very very rare) give birth to more airbenders except the next Avatar, who would lack a living mentor for that element, be unable to give birth to more airbenders themselves, and have a massive target on their back from the people responsible for killing all the other airbenders.
So, unless the Harmonic Convergence event affected Caryn and/or Filbrick when it happened for Korra, or the planets somehow aligned in an unprecedented manner, Stan's not going to be an airbender without at least one parent from a line of airbenders. Hey, in Gravity Falls, anybling can haplen, I just find it highly improbable. For Mabel to be a firebender, that means either her mom or dad had to come from a line of firebenders.
Bending affinity comes from personality, mostly nature with a bit of nurture. As a general rule, free-spirited, flexible, and unmaterialistic people tend to make for better airbenders; calm, easygoing, and generous people tend to make for better waterbenders; stalwart, logical, and direct people tend to make for better earthbenders; determined, passionate, and energetic people tend to make for better firebenders. If you think of it like Tomodachi Life types, airbending is energetic/ outgoing, waterbending is easygoing/considerate, earthbending is reserved, and firebending is ambitious/confident. But bending can also match up with different personalities in unexpected ways. For example, a free-spirited earthbender may struggle with traditional earthbending, but do well as a sandbender because sandbending borrows a lot from airbending techniques.
Airbending is particularly sensitive to personal philosophy, as it is the most spiritually oriented of the types and therefore benefits most from an ascetic lifestyle-- but there are ways to use tools to augment airbending deficiencies if you can airbend. Avatar Kyoshi's mother Jesa was an airbender who left the life of a monk to found a criminal enterprise with an earthbending thief, but she knew how to use fans to airbend very effectively despite her violent and materialistic lifestyle degrading her ability to use airbending. It's a skill she passed on to Kyoshi.
What this is all getting around to: Airbending Stanley comes from airbending Caryn. Caryn didn't have powerful airbending due to her lifestyle as a fake fortune teller, but she was able to use a deck of oversized novelty tarot cards to direct air around and augment her bending. Since she wasn't doing combat, she only needed subtle effects anyway-- a slight gust of wind to make a room feel a little chillier during fortune telling, or a puff in the ear to startle annoying customers or cashiers when she's shoplifting. She teaches Stan all her tricks and it's a very sweet series of bonding moments that Ford has festering jealousy of. (Stan absolutely did not cry after Caryn's death when he learned he [or well, Ford, technically] inherited her favorite set of tarot cards. Not one tear. You can trust him when he says that.)
Whether Filbrick had latent airbending abilities that he never used or was a non-bender isn't clear. Either way his philosophy is more along the lines of "Bending, eh? How about I bend my finger around the trigger of this gun?" (in a world with metalbenders, guns made with plastics have far more development and utility than in our world). Much like canon, he's way harsher on Stan than he is Ford, but with the extra layer of being distrustful of benders (he does love Caryn in his Filbrick way, but her actions as a kleptomaniac and fortune teller don't exactly disprove his suspicion here either) and seeing airbending as something Stan uses as a crutch or shortcut. Since Ford doesn't have access to that shortcut, he's clearly the superior twin, both deserving of more effort and care and capable of far more than his bending brother. Much like canon, this contributes majorly to Ford's massive inferiority-superiority complex.
Mabel's grandma comes from a firebending family. There is absolutely tension between firebenders and airbenders as they've historically come to blows-- depending on who you ask, it's either the airbenders' fault for not being able to honor their treaties, the firebenders' fault for refusing to compromise with or respect other benders, or the fault of a complicated set of systemic prejudices rooted in imperialism for assigning morality and behaviors to bending styles. Filbrick was Not Impressed with Shermie's choice in wife. Shermie shrugged and basically said "fine, disown me then" and so Filbrick did that. Once Filbrick kicked the bucket, Shermie and his kids slowly made their way back to his surviving family, though Shermie's branch of the family tree remained somewhat distant. But hey, they trusted "Ford" enough to send the kids over for the summer, so that's not nothing. We're mending the family tree here!
I like the idea of Lil' Gideon being an Amon-like figure, claiming to be a non-bender in order to puff up his feats and make himself look more talented when he's actually a waterbender, more specifically with a bloodbending specialty. Journal 2 has a lot about bloodbending and this was not a great thing for a 5 year old in a dysfunctional household to learn about, it turns out. The amulet, rather than granting telekinetic abilities, lets Gideon use waterbending abilities all the time that would normally only be available during a full moon. Instead of using telekinesis to attack Dipper, he was going to bloodbend Dipper into going on a rampage and attacking people so Dipper would ultimately end up getting arrested and discredited. So breaking it is still a significant depowering and constitutes revealing him to be a fraud-- though it's not the breaking point, as the townspeople bought his story that "poor wittle ole me" only just found out about the bending and don't think he's specifically a bloodbender. When it's a full moon, he remains as much as a threat as he was in his introduction. The cameras, on top of catching his fraud like in the canon Gideon Rises, also catch him bloodbending. That scares the crap out of everybody and thus discredits him. Stanchurian candidate happened because Gideon figured out a way to amp himself so he could bloodbend without a full moon, and used it to pilot his dad. This also has major consequences down the line, though at least he's trying to be a good person by the end.
On the flipside, the incident with Gideon is also something of a vaccination against Bill's actions in Sock Opera-- Dipper is way way more suspicious of talk about puppets from the get go, and so, even sleep-deprived, he immediately susses out that Bill means HIM when Bill requests a single puppet and refuses the deal. And this would be the biggest point of canon divergence in the end, since Bill not breaking the laptop means the Mystery Twins not finding out about McGucket Labs meaning that the Society of the Blind Eye is still out and about with the memory gun by the time Not Who He Seems hits (though I can't imagine it would be too fond of the FBI poking around the area. That would be one hell of a twist-- the SotBE wipes the FBI's memories instead of Ford, perhaps even well ahead of Ford's arrival, and everybody is wondering why the hell the government guys poking around the area are suddenly disoriented and forgetting everything.)
I like Pacifica being a non-bender who feels that she has to fake bending to be accepted amongst her prestigious peers, who have all received top-notch private tutoring and so are genuinely among the best of the best benders. The twist is that her parents are ALSO non-benders, and Nathanial Northwest wasn't a bender either. They compensated with technology and weapons-- Pacifica herself keeps firecrackers on hand to fake fire-bending. A lot of Northwest Mystery Mansion Noir here is deconstructing discrimination against non-benders and prejudices relating to bending styles as a whole, with Pacifica finally coming out as a non-bender to the public and letting non-privileged people in to save everybody.
Wendy I think has a good disposition for sandbending (sawdust-bending? Is that a thing?), so yeah, agree on the Earthbender thing. She's firm in her beliefs but also willing to adapt and adjust in the face of new situations or crises. Also the idea of Robbie challenging Dipper to an Agni Kai is hilarious (and Dipper being like "wait I'm a nonbender is that even possible" while Stan is like "kid he doesn't care you gotta stand up for yourself and be tough"). May I add Rumble McSkirmish being a spirit who happens to be really, really into fighting games to the point of changing himself just to integrate into an arcade machine? GIFfany could have been in a similar boat, or alternatively she was obsessed with Soos in general and would have taken whatever form was necessary to make contact with him (the dating sim was just the option that presented itself most obviously to her).
This was fun to gnaw on. Sorry for the massive post! Feel free to correct me if I got something wrong!