1) But what's your justification for thinking of them as totally unrelated? As cheerleaders/parents of cheerleaders, we have a considerable bias in thinking of splits as totally nonsexual. However, twerking and splits are both performed in strip clubs, and both have the potential to generate sexually lewd comments. As I've said repeatedly, context is what matters. Biologically speaking, the rear end isn't any more sexual in nature than someone's eyes, mouth, ear, foot, etc. Additionally, based on everything that I've seen on the internet, nonsexual pictures of girls doing the splits in skimpy clothes (or even non-skimpy clothes) generate considerably more sexual comments than does a video of friends twerking (which generates comments more grounded in racism than sexuality).
2) It wasn't my intention to put words in your mouth, but when you justify a ban solely based on the vague pretext of "Christianity", it does carry the insinuation (irrespective of your own intentions) that those who don't agree with such a ban aren't, at least in your eyes, following sections of Christianity as well as your own gym. I can understand that you intended the message to be "We don't really approve of twerking based on our personal interpretation of [insert Bible verse that discourages sexually explicit behavior]". It may seem kind of pedantic to make such a fuss about phrasing, but it's important to remember that there are a lot of people who have had a lot of negative experiences with rude and judgmental "Christians" who try to defend their poor manners with "The Bible says that you're sinning".
3) The "barely any clothes" thing again brings context back up. I'm sure you're aware that many, many uniforms could be considered skimpy by the general population, including your own gym's (note: I don't actually believe this). I really do think it's admirable that a gym is trying to prevent the sexualization of children on social media. I just don't see how this solves that problem. You'd need to ban ALL content (like splits) that can be sexually exploited (which would be virtually impossible), or just put more effort into teaching the value of maintaining strict security settings so that the creepers of the internet won't have access to any of the exploitable private content in the first place. I really, really do appreciate the intention of this ban, but having a blanket ban on twerking isn't an effective solution to the larger issue of privacy abuse.