So I want to preface my take on this with some questions of my own. I don't care one way or another how you answer these, but if you're first instinct is to say "no" to any of them, I want you to seriously consider what, exactly, about these situations feels different to you.
Would you have the same negative reaction if this was about a One Direction fan? Would you have the same reaction if it was a Beyonce fan? A Deadhead? What if her fandom of choice was Star Wars? Harry Potter? What if she followed sports this closely?
The fact of the matter is, being this obsessed of a fan of something, while maybe not the norm for every fan, is not unique to ARMY, or KPop, or music, or anything, really. But most harshly negative reactions center on boy band fans because, rightly or wrongly, that is viewed as the territory of teenage girls. Society loves to mock whatever teenage girls are into as being a waste of time or money or proof of lack of intelligence (see: people's response to PSLs, but nobody having the same response to the IPA beer craze, or the "everything bacon flavored" craze). I honestly doubt she's spent more in the course of her time as an ARMY than an obsessed pro-sports team fan spends on tickets and merchandise in the same time period, but that's considered a perfectly acceptable (if quirky) interest for any respectable adult to have. What, fundamentally, makes them different?
Ultimately, building your identity around being a fan of a particular band is no different than any other means of "picking your tribe," which is why it is so common among teenagers to start deeply identifying with a group. Something about that group - be it their sound or their message or their fandom's "reputation" - either speaks to you as you are, or speaks to you as you hope to be, and you are choosing to associate yourself with that group because it helps with starting to build an image of who you are as a soon-to-be-adult beyond the tastes and interests your parents funneled through you as a child. Believe me, I'm a child of the 90s, it said a Lot about you if you identified as a Backstreet Boys fan rather than an N*Sync fan, and your favorite member said even more. Not that this is all that goes into it, but most of the time these group stereotypes are really well known, so they do work as a sort of shorthand for "this is what I like and value, if you like and value these things come be my friend." Some people need that identify function more than others, others don't need it at all, others need it but grow up and out of it, others don't, but none of that is any more outside the norm than when children or teens for a hyper fixation around... idk, Ancient Rome. Or dinosaurs. Or horses. I feel like everyone knew or knew of a horse girl. We knew what it meant to be a horse girl. She knew what it meant to be a horse girl. In the US, even someone who doesn't follow sports probably has some sort of sense of what it means to be "a Yankees fan," and if someone is introducing themself as a Yankees fan, they're likely aware of those implications.
A whole sociology paper could be written on how K-Fandoms differ from I-Fandoms, but I'm not convinced it's innate cultural differences that are causing this. Rather, I think they're more practical consequences of Korea being physically compact and creating much more opportunity for both extensive inter- and intra- fandom interaction and contact.
But in the end, nothing I've seen from KPop fandom is more extreme or more toxic than what I currently see in western music fans, or what I saw from music fans in the 90s, or what I currently see from sports fans.
Finally, just as practical context: a lot of what's going on with "official" membership and quizzes and proof of purchasing albums and such is that it's a very practical response to a few problems within K-Fandoms. Fandom membership usually allows early purchase of concert tickets (for Korean dates), entry into the audience for music show performances/tapings of your favorite group and the ability to enter the raffle for events like fansigns. Some events like award shows will have designated sections for fans, and membership allows them to determine how many to let in and where to sit them so that the same fandom can be grouped together. For small fandoms, the membership fee essentially becomes a rubber stamp to say "okay, you're willing to spend $25 on this, you're probably not a bored troll who just wants to cause trouble." When groups get bigger is when fan clubs start imposing stricter guidelines, because that's when scalpers and antis become a problem, and the sheer number of fans means there needs to be some method if divvying out limited numbers of tickets beyond first-come-first-serve.