That's right people, some idiots are complaining about Mabel being "too feminine and boy crazy" and "always needing her brother to save her". Again, what? What version of the show are you guys watching?
Mabel saves herself, others, and her brother just as often as Dipper saves her, himself, and others. Dipper and Mabel have very similar yet very different personalities. Mabel is more likely to listen to her heart, which comes in handy on multiple occasions, but she is still intelligent. Dipper is more likely to listen to his head, but still follows his emotions at times. Both characters have flaws, and strong points, and both support each other. Mabel can be selfish at times, and it is true that Dipper sacrifices a lot for her, but he is self-centered at times as well, and Mabel does things for his happiness as well. More often than not, the twins work together, to save each other and those around them, not Dipper always saving Mabel like some insinuate. In fact, one of the lines that probably sums up the show the most is when Wendy, in one of the episodes of Weirdmaggedon, Wendy says she has seen many amazing things that summer but "nothing more amazing than you and your sister" (I wrote that by memory, so if I'm wrong, correct me, but my point still stands). Which is most of the point of the show anyway.
One of the complaints about her is her girliness and apparently being "stereotypical". Well, nothing is stereotypical about this character; she is fun and creative and random and crazy, and totally unpredictable. She is also based heavily on Ariel Hirsch, Alex's twin sister, so most of her personality is derived from a real life person. When you say that Mabel is a stereotype and a character that would never exist in real life, you are straight-up insulting a woman who exists. This also includes Mabel's obsession with boy bands, something that Ariel and many other pre-pubescent, and teenage girls are. That's not just a stereotype, it's true for most girls.
Another thing that I actually only found in one post here: http://canonicalmomentum.tumblr.com/post/98300310147/canonicalmomentum-what-the-fuck-was-that complains about the episode "Soos and the Real Girl". Mostly about how Soos is told he needs to find a girl to bring to his cousin's...I think it was a wedding or engagement party or something? I've only seen that episode once, so forgive me. Either way, he is basically told he needs to find a date, presumably female (which of course is so homophobic some how, even though as a straight girl, if I needed a date for something, although I don't know why I would, people who know me would say to bring a guy, not bring a date like a guy or a girl, not because they're homophobic or I am, but because they know I'm straight) and when the kids try to help him with these stereotypical tips of "make eye contact" and "be confident" he messes up horribly, misinterpreting what they're saying. Of course, I'm sure someone will complain that some girls don't like confident guys and prefer shy, awkward boys and presuming all girls like this one type of guy is sexist or against anti-social people. This is also the episode where Soos buys the dating sim with Giffany, and as someone who recently started playing dating sims because I find them fun (despite the fact that I have a boyfriend), I am totally okay with the fact that they make fun of people who play them. Either way, this person in particular was complaining about the fact that no one mentions the fact that he shouldn't go up to random girls and hit on them, well, he ends up finding his love interest by NOT doing that anyway, so...And on top of that, I don't really see the issue. If a guy politely walks up to me and is flirting with me, I personally wouldn't mind, and if one of those girls had said "go away I'm not interested", knowing Soos, he probably would have. I think it's only creepy if you walk up to a female and say sexual or inappropriate things, which of course, Soos didn't, or persist after a girl makes it clear she is not interested.
And the whole "you're probably a girl" joke in the same episode isn't transphobic or anything like that. It's not supposed to be a joke at the expense of the person he's talking to, but rather, to show how socially awkward Soos is in the fact that he probably shouldn't say something like that to them.
Honestly, this show is pretty progressive without being super in-your-face about it, a lesson a lot of Tumblr could take up (-_-"). It really does show that gender confines do not define a person, that we can break away from the norm and be who we want to be. The cartoon depicts Mabel turning down a "nice guy" because she does not like him romantically and should not be obligated to date somebody just because he is nice (which it turns out he isn't), and also learning that she needs to fight her own battles as well as episodes that show that she can be just as strong as her brother. Her using her emotions more than her brain is not saying that girls are overly emotional and stupid and can't be trusted, especially when it comes in handy and Mabel is actually pretty smart. It is just that she prefers to have fun and be nice than stress herself out. She isn't always the most logical, but she is dumb either. Wendy, on the other hand, is logical while still retaining a fun persona and is more of a tomboy, without being the stereotypical tomboy trope of a masculine girl who hates everything feminine. In fact, I think she is the most bada** (pardon my implications of swear word) character in the show.
Girls are not played off as useless or unintelligent in this show, but have a variety of personalities, just as real people do, and a lot are based on people Alex or other workers on the cartoon knew. So, no, it is not sexist, intentionally or otherwise.