Look, this is definitely me putting my own positive spin on the game, and I could be ignoring stuff to put my opinion in a better light, but I always felt like a lot of the group interaction revolved around the point that really, outside of the investigation group, none of these people would have had any reason to interact, particularly people like Kanji and Rise. But it's the fact that they're hanging out with people they're unused to that makes them stronger characters.
In regards to the teasing directed at Kanji, his reactions are based around the fact that he's never received that from someone who is still his friend. He's not used to playful teasing. His previous reaction to anyone saying anything about him was to act tough, so it's no surprise that his reactions are all dour. He's still learning how to deal with stuff and internalize it, and that ultimately makes his character stronger. Rise and Yosuke tease, but they're ultimately loyal to the group, and that's a key undercurrent. I never got the feeling that anyone was being outright rude or disrespectful. There's definitely at least one case of every member sticking up for another member at some point.
The characters in Persona certainly have their flaws, but I feel like the game rationalizes them and makes them core to the characterization. I know people on this board have a problem with the way Yosuke acts, but I think that in many ways, this is intentional. Even at the beginning of the game, Yosuke is shit on by everyone around him and people definitely think he's a creep. He puts out an annoying little brother vibe. And this is even reflected by his own shadow. It's part of who he is, it's how he acts in the world. But you do see his personal side and how loyal he is, and really he just wants to be accepted despite his immaturity. I think we all know people like that, and many of us are like that ourselves.
This goes for Rise too. She's an Idol; being playful and teasing are part of the job, it's how she's used to interacting with people. It'd be shocking if she just dropped that part of her character entirely. The other characters even call it out. They recognize when she's being like that. The game realizes that these characters have flaws, it's not like everyone ignores it. That's what made it feel real for me. Think about yourself and your own friend group: hardly ever do we just open up entirely and then solve all of our internal flaws and quirks. We open up in small amounts, often in private, and rarely to the entire group. We put on a face, but as we gain trust, we show deeper sides of ourselves. Persona is a game entirely about this concept, so it's unsurprising to me that this would happen in the group itself.
And yes, the writing isn't perfect. There's certainly some parts that don't mesh with others. But this is a game written and designed by multiple people, so it's not surprising. It's far more consistent than I've seen in other games, so that's why I love it so much, I guess.