I think it is far more simple than that. I think these people just aren't closer than coworkers in most cases. Sayu was only around 3 months, Doki always felt like she got along better with people outside of Nijisanji. People need to be looking at this from the perspective of coworkers than them actually being friends. With how many of them there are and all across different timezones, it just is not likely they can all be close.I have given up listening to any of their supposed claims but instead focused on their actual actions. As it stands, I haven't seen anything related to Matara and Kuro showing any support for Doki or Sayu. Meanwhile they've eagerly shilled Quinn, who went on his PL to shit on Sayu/Zaion.
For all I can gather, the clique isn't some hard rule but more of a peer pressure group. If you're playing along, cool. But the moment you don't join in their stupid fucking tactics, you started to get ghosted and isolated. Matara likely turned down some of their initial stupid shit but then bent the knee because she's soft like that, as she's a dumbass that was afraid of speaking out against commie ideals because she was afraid she'd lose her commie friends. They were likely fine with Selen when she started because she's ultra carefree but she slowly got isolated because she was becoming too important and made the clique girls feel insecure. Part of it might have been them trying to leech off her for growth but they realized a lot of dragoons don't give a fuck about Elira or the 2 flip monkeys so there's not much left to leech. It's all very "high school-ish" behavior.
Even HoloEN have people they are closer with than others. It took Bae and Kronii Japan trips after like 2 years to finally be comfortable with each other, for example, and they are in the same gen.