Fraggle Rock is an egalitarian society (it can also probably be seen as being an example of idealized socialism, but that is for another post). And along with being an egalitarian society, it is also a society that eschews gender roles in determining which Fraggles do what duties. Boober isn't automatically disqualified from sock washing duty because he is a boy Fraggle - never mind the fact that washing socks shouldn't even be a concern because the Fraggles don't wear them. Red isn't barred from her more adventurous and athletic pursuits. Both are celebrated for what they can do, and what they enjoy doing. So Boober gets to talk about his dreams being prophetic nightmares as he washes socks without it being mock-worthy, and Red gets to be at times abrasive and the best swimmer in Fraggle Rock without her femininity being called into question. They are viewed on an individual basis, separate from other concerns. Sure, Red learns that she can't do it all on her own all of the time in "Let The Water Run", but that isn't based on the fact she's a "she"; instead, it is because none of us can be fully independent all of the time. We all need help from family and friends. There is no having it all and doing it all, even for an intrepid young Fraggle.
This idea of gender noncomformity is further shown in Wembley, whose name is turned into the word "wemble" - a word that literally describes indecisiveness. Wembley wembles on everything, even on which of his two identical banana tree shirts to wear on any given day. And that is partially because Wembley is a bit wishy-washy, but also because Wembley is in tune with emotions, and he doesn't want to hurt any one of his friends. Because even if he says "yes" to one Fraggle, he has implicitly said "no" to another one. That sort of emotional openness is not often attributed to boys; and even though Wembley's wembling is at times irritating to the other Fraggles, it is still not truly seen as an undesirable trait. And it does demonstrate that an emotionality is not only acceptable but desired in people, though maybe not to the extent Wembley takes it (just like with the other Fraggles). Wembley's also the Fraggle who has a crush on Red - which is kind of like Xander's crush on the more assertive, more athletic, in charge Buffy. Both of these roles demonstrate that not only can guys still be fully and wholly guys with nothing to be ashamed of even if they aren't the Arnold Schwarzeneggers or Sean Connerys of the world, but girls can still be wholly girls - and not just considered nonsexual because they deviate from the gender norms - when they aren't fully engaged in the passivity we normally see as the ideal for women.
Mokey Fraggle and Gobo Fraggle are the two Fraggles that best fit normal gender norms in that Mokey is artistic and gentle and most obviously the 'den motherish' one out of the five prominent Fraggles. Gobo is head-strong and adventurous and the de facto Fraggle leader. But even with that, both of them help balance out this gendered equality; boys and girls can still be interested in traditionally boyish and girlish activities, as long as boys who are more into "girlish" activities are still seen as equal and girls who are more into "boyish" activities are seen as equal, as well as the traditional "boyish" and "girlish"activities existing on the same plane as well. Mokey and her activities are just as respected and honored as Gobo and his activities. And the same is true for the rest of the Fraggles. Wembley's job of sounding the Fraggle Fireman siren is just as important as Boober's sock washing and cooking jobs, which are just as important as Mokey's job of picking the radishes, which is just as important as Red's job of cleaning out the Fraggle pool and teaching young Fraggles how to swim. And that - along with the grander theme of Fraggle Rock, the one about three separate societies coexisting in a symbiotic fashion even as the residents of each society are ignorant of their interconnectedness - is the enduring message of Fraggle Rock. That each person should do what they love, and be respected for it.