Disclaimer: By no means do I consider myself an expert on feminism or feminist discourse. I'm not even comfortable enough with the subject to claim I am particularly knowledgeable. In fact, I know very little about the history or various waves and shades of feminism that exist today. I am confident enough, however, to feel like I can pinpoint feminist ideas when I see them and can thus point them out when I do. So, while going through this article, please take my words with a grain of salt and feel free to correct me if you think my beliefs and assumptions are wrong.
As it is first introduced to its audience, Asobi Asobase seems like it isn't going to be all that different from a lot of the other slice of life, school girl comedies that litter the anime landscape. Starting with the show's opening, it plays with a lot of very recognizable themes and concepts that are typical of these kinds of shows. You have three attractive young girls who clearly seem to be having fun and working together to make their high school experience memorable as they doodle on the classroom chalkboard to spell out the title of the show. As this opening goes on, we see various pieces of imagery that depict these girls as cute and innocent with their off-white dresses, longing expressions, and almost infantile playfulness. Yet, as such depictions usually do, there is a darker undertone to these cute, sweet, and pure images that speak to the objectification of these characters. With this kind of presentation, blatant as it might be, there is this underlying idea that these girls are perfect and beautiful strictly because of their purity and naive interest in/longing for something that is lacking from their all-girls paradise. As to what that something could be, the male gaze that is rampant in this opening and the playful grin at the mere mention of the word "kiss" make it pretty clear that the one thing these perfect girls lack in a man in their life to fill that hole in their lives and hearts that they clearly don't/can't understand themselves. This kind of blatantly sexist imagery is, of course, nothing new, given the tendency of various anime magazines to feature such titillating innocence. The idol industry as a whole is almost built solely from reveling in these ideals. So, it's not exactly hard to draw some parallels between this opening and that industry as the girls sing the opening and offer the audience poses that you'd only see in a staged photo shoot. If all this sounds like a bit much, though, you'd be absolutely right because Asobi Asobase is nothing short of a lampoon of the blatant and rampant sexism present in these kinds of all-girl slice of life comedies.
In its attempts to lampoon and subvert its genre and its inherent sexism, though, Asobi Asobase also manages to present a bizarre and disconcerting brand of feminist ideals that seem to simply state that women can be just as gross, insensitive, and petty as their male counterparts. Whether it's Olivia's unique ability to dig herself into a hole she'll never escape, Kasumi's overly-aggressive competitive nature, or Hanako's selfish desire to shit on anyone's happiness just because she's never actually tried to work for her own, the show does a fine job tipping you off to the fact that these girls are not nearly as "pure" or "innocent" as that opening made them appear. Yet, at the same time, the show bears no illusions that these girls are trying to be anything other than themselves. They're selfish, rude, impulsive, and intolerable but are very much in control of their own fates.
While the show generally uses these traits in skits and gags that make the girls deliberately unsexy or unappealing, it also works to define their various problems and hangups that make then no better and no worse than the few male figures that dot the show. There is no real concept of one person being superior to anyone else, regardless of gender or social class. The main character of Hanako, for instance, is born from a wealthy family that pampered her and raised her to believe that she could and should have anything she wants just because she wills it. All her money and upbringing do for her is foster that ludicrous idea that she shouldn't have to work or try to become popular or get a boyfriend which results in her attaining neither. Rather than growing up and trying to actually be someone worthy of a large friend group or a boyfriend, though, she just lazes about, bemoaning the things she doesn't have and resenting the people who actually worked to attain their happiness. So, regardless of her family's wealth or status, Hanako ends up being no better than Olivia who starts the show acting like a foreigner that can't speak Japanese well when, in reality, it's the only language she knows. Rather than actually studying English to keep her ruse going or just owning up to the fact that she was just messing with Hanako, Olivia abjectly to own up and ends up digging herself a deeper hole as the show goes on. Then, of course, there's Kasumi who is so quiet, reserved, and afraid of what other people think that she basically sacrifices her hopes of getting her grades up for the chance at some semblance of friendship with these two girls who treat her like dirt. Yet, like many otaku, she's no less powerful than her comrades when the chips are down or they attack something she's passionate about, at which point she becomes the only person capable of cowing the selfish Hanako and lazy Olivia. So, in a weird kind of way, these girls manage to be equals and friends even though they're all terrible people that ceaselessly drive each other up the wall.
At the same time, though, the same can be said of every character in this show. Every other girl is just as self-centered and petty as Olivia or Hanako. Every guy is just as crass and perverted as Kasumi is beneath her inability to communicate with the opposite sex. Not a single teacher is any more wise or considerate than their students. Now, sure, this kind of acknowledgement that all people are equally terrible might seem a bit cynical or over the top, because it kinda is. Yet it's no less true to some degree. Everyone on this earth has some kind of quirk, kink, or hangup that makes them different from others. Sometimes that difference can be just as simple and overtimes as complex as something only an eldritch god could imagine, but there's a weird kind of equality in that acceptance that we're all weird and terrible in our own ways. Though I'm relatively certain that Asobi Asobase never meant to make itself something worth some feminist analysis, the equity of power and disgusting behaviors seen in all its characters does speak to a concept I often see in feminist discourse: the equality of freedom, rights, and opportunities regardless of race, sex, creed, or code.