I think that whether you cringe at something or not is an individual problem, and no matter what I say here, you probably won’t stop cringing at the fandom. But I’ll answer your question.
It’s not rude. I actually ask myself that question sometimes when I get annoyed. You know, I’m 26. I’m probably older than the majority of the fandom, especially here on tumblr. There’s a lot of obnoxiousness and immaturity going on in the fandom at all times, and sometimes it gets annoying, particularly the immaturity. But your description—”a bunch of obnoxious attention-seeking teenagers. They exaggerate, overreact, get over-excited about the silliest things“—doesn’t really describe GazettE fandom, it describes people in general, and teenagers in general. Regardless of fandom, most people will at times get obnoxious and seek attention and they’ll overreact and be excited about things other people will find silly.
The amount of obnoxious people you find in a fandom is directly proportional to the fandom’s size. Gazette fandom is fairly large, but it’s not a homogeneous blob. You can’t point at the fandom and say it’s obnoxious when there are thousands of people here and they’re all different. Not all people are obnoxious or pleasant. Some people are obnoxious sometimes, and sometimes they’re perfectly nice. Some people seem wonderful to some but awful to others. You’ll always find people you don’t like here, as you will everywhere. There are people in the fandom whom I don’t like, or people that are annoying to me. I don’t engage with those people. I engage with people I find interesting and I’m glad I do so, because I’ve found some really nice friends here.
IRL, I don’t have anyone who enjoys the same music as me. Most of my friends are into stuff like black metal, and won’t listen to a band like Gazette. They’re also not in the fandom of any band and don’t understand what that means. So IRL, I don’t have anyone who understands how much I love this band or who even understands the excitement about having a new single or album out. People in the fandom understand that well, and I enjoy sharing that excitement with them.
I think there’s one very amazing thing about all art forms, and music in particular. For you to profoundly enjoy music it doesn’t matter if you’re mature or immature, or if you’re a nice person or an obnoxious person. None of it matters. You just have to like it and enjoy it, and that’s all. And no matter what kind of people we are, in this fandom we all share this one trait. We all love Gazette.
I think that people who gather into fandoms might be a little more into something than other people, though. Maybe we care a little bit more. Maybe we love a little too much. That’s why fandoms are so enthusiastic. And sure, I find it a little annoying that I’ll see hundreds of edits of one picture a few hours after it’s released. I get annoyed when people are rude and insensitive when things like Kubana (un-)broadcast happen. My heart sinks a bit when people send unfounded hate to Aoi and Ruki on twitter. But when things like that happen, I remember that underneath it all, we love the same thing. It doesn’t matter how old you are or how long you’ve loved the band: when it comes to the love we have for the music, we are all the same.
When in one of those bad moments I ask myself, “What am I even doing in this fandom?”, I take a moment to look around and remember that there are thousands of people all over the world who love this band just as much as I do, who get excited and happy and sad and angry about them, whose day gets a little better when they listen to the music, who are maybe even still alive because this band exists. Maybe I wouldn’t like all those people if I met them, but in this one thing we are united. And I think that’s pretty amazing.
So I don’t “put up” with the fandom, I’m glad to be here. It might be ugly and dysfunctional at times, but more often than not, it feels like a second home. I’m sure that to some people, it feels like the only home. And like any home or family, it may seem awful when you look at it from outside and only see the broad strokes. When you look at the details, things might seem different.