Gosh - sounds like a very internally competitive gym that pre-teen girls would have that attitude towards potential new teammates/friends

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Yeah, my DD makes assessments on new people's abilities (what are they good at, bad at, etc.), but is usually way more interested in learning about them as a person (where do they go to school, how old are they, what are they like) and figuring out if they are nice or not, than she cares about how them joining the team will impact her "status" at the gym. That almost sounds like the Abby Lee Miller dance moms pyramid, but only for gymnasts

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Well, I am not the author of the post you refer to, but I "liked" it.
My DD is in a pretty darn competitive gym with lots of great girls. My DD is also very introverted and is quite slow to warm up to people. Anyway, DD had been with her same training group for 1.5 years. One new girl started and at first my DD really did try to get to know her a bit, and thought she was ok. They were never mean or exclusionary to her, to my knowledge based on chatter from the kids... I would hope this to be the case everywhere. And if it wasn't, I'd have hoped that the mom wouldn't have let her come to DD's gym.
As soon as she "officially" started though, said girl immediately started telling my DD and teammate's all about how their gym works, and in the process, actually really offended and hurt my DD.
Now, said new girl didn't necessarily KNOW what she said would be/was hurtful. DD made an initial attempt to correct the girl, she held her ground, and a bit of preteen/early teenage BS got started. New girl just competed a level above any other girl in the group's highest level... this does not help the situation along. Add in another new girl who competed an even higher level and knows other new girl... Well...
So, the above example is the context which I took with the original post you quoted. Not so much some gym-mandated thing like dance moms... But girls seems to understand their "place" in the gym... One is great at beam, one is a great all arounder, one always gets her bar skills first, so-and-so is "lower" on every event, but is a great cheerleader to her teammates. They each have a role, which seems to peak in importance around middle school age. So plop in a few new girls to a small, tight-knit group of girls, and it's a recipe for drama. It doesn't always happen, and I love it when that's the case, but it sets the stage for it. My DD has now officially been on both sides of it. I don't think it's NICE, but it happens.

And I don't think it reflects the kids' personalities directly, but rather their insecurities.
To OP, I'm glad your DD is so welcoming. I hope that never changes.

It's hard whenever they get to know each other and then someone moves on. We've made an effort to remain friends with old teammates from all over (some or of state). With effort and FaceTime, etc, it's possible!