Fraggle Rock/WMG

The theme tune inspired Daft Punk to write Robot Rock
Just listen to them both. Don't they sound similar?

Fraggles reproduce in an unusual way
Junior Gorg has a mother and a father. So does Cotterpin Doozer. So Gorgs and Doozers must reproduce like people. But none of the Fraggles have parents. The only older Fraggles are Uncle Traveling Matt and The World's Oldest Fraggle. Obviously, Fraggles are like mayflies, salmon, and 17-year cicadas; creatures that die right after reproducing.
 * Then again, the opening theme shows a Fraggle holding a baby Fraggle.
 * It may also just not be a part of Fraggle culture -- if generations live and play together age might make less of a difference. Mokey's both more mature and larger than the rest of the Fraggle Five, and is accorded a bit of respect; she could be double their age for all we know. She could even be somebody's mom.
 * It's worse than that. "Gorg" is apparently a species, yet there are only Ma, Pa, and Junior. Not enough for a species. What's more, "Junior" merely indicates that Junior has the same name as his father -- to wit, they are Pa Gorg and Pa Gorg, Jr. ... SOOOOOO at some point Ma and Pa will have another, female child (who we will call Juniora). When Junior and Juniora become adults, Ma and Pa will spontaneously die; Junior and Juniora will marry, have a male child they will name Pa, and the cycle will continue. Millennia of inbreeding explains a LOT about the Gorgs.
 * Maybe there are other Gorgs around, but we can't see them because they haven't been putting on the radish "youth and beauty cream".
 * Maybe there are other Gorgs around, but they live further away; honestly, they could just live a mile away from Ma and Pa and we'd have no clue they existed. Certainly the Gorgs seem to be planning on moving somewhere when Sir Hubris arrives, so the garden can't be the limits of the Gorgs' world.

Fraggles and Doozers evolved from a common ancestor
The ancient Fraggles ("Mokey Then and Now") as well as a faraway group of modern Fraggles ("Fraggle Wars") are far more serious-minded than the group of Fraggles we are accustomed to. Meanwhile, the Doozers have a legend of a Doozer who, by singing and playing all day instead of working, became a Fraggle.
 * The second part, at least, was Jossed - Cotterpin tried it, wanting to become a Fraggle. It didn't work, because it was just a Doozer boogieman story.

Hobbits evolved from Fraggles
Fraggles are pure, good-hearted, and in love with life in addition to being physically small. They are somewhat gluttonous, find any excuse to sing and play, are committed to their traditions, and show little to no interest in the outside world, save for a few. The idyllic Fraggle Rock is pretty much an underground Shire, when you look at it closely. "Gobo" even looks like it could be a Hobbit name. Perhaps the Bagginses are descended from his family?
 * Since the Third Age is supposed to be aeons in the past and Fraggle Rock is set in the eighties, it's more likely that Fraggles evolved from Hobbits.

Cantus and Convincing John are related
They’re both extremely charismatic, they both possess strange powers that no one has ever been able to fully explain, and their voices are very similar. What led them to take such divergent paths remains to be seen, however.

There was an entire backstory depicting the history of the Gorgs and the Doozers that the show never got around to addressing before its cancellation
Discussion on a (now sadly defunct/replaced) Fraggle Rock fan forum suggested that the shipwreck found off the coast of wherever it is that Doc lives (the La Gorgola), the one that contained among its treasures a Doozer helmet made into what was either a (bulky but human-sized) ring or possibly a necklace bauble for a very large creature, was evidence that both Gorgs and Doozers traveled to (and in the case of the Gorgs, through) Fraggle Rock from the world of the Silly Creatures, presumably entering via a larger hole that the current one may be a boarded-up remnant of. It was also speculated that Pa and Ma Gorg or their predecessors were the in-universe inspiration for Gog and Magog, an entity or pair of entities sometimes depicted as one or a pair of giants. This, coupled with the strong possibility of Sir Hubris being a human (above) and human legends of giants in general, may point to the show's creators having planned a backstory for the Gorgs (and possibly Doozers) that they either simply never got around to addressing, or wanted the fans to work out for themselves.

Fraggles are monotremes
An idea that was also floated on the above mentioned fan forum, and based on a couple of known qualities of Fraggles, namely that they appear to have mammalian fur (and possibly beaks, much like platypi, though that's open to interpretation as it could just as easily be simply a factor of the way the puppets are designed/made), and that they supposedly lay eggs (a fact that turned up mostly in supplemental material, though the Storyteller did mention a fraggle as having been "hatched" in one episode).

Beluviouses are a survival mechanism
"Beluvious" being the in-universe word for a Fraggle's tail-tuft, which flares out when said Fraggle is scared or startled. Beluviouses are, notably, usually the same colour as the "hair" on a Fraggle's head. This lead to the speculation (once more, on the above-mentioned forum) that it served a similar purpose to the detachable tail of a gecko, except that instead of predators latching onto and causing the loss of the entire tail, predators are simply fooled into going for the nearer fake "head" at the tip of the tail as the Fraggle turns to flee, ending up with nothing but a mouthful of fluff (and if you've ever tried to get hairs out from under your lip and between your teeth, you know how distracting this can be), which the Fraggle most likely then re-sprouts over time.