That London School of Elite Snobs thread was baseless as well. Reading it did annoy me at first because while I've been here I've met so many different people and so few of them fit that description. That doesn't mean nobody does - but you're almost certainly going to find at least some "snobs" anywhere you go.
Although I would actually say there's a positive minority at LSE compared to other comparable universities. Especially with there being so many people from abroad: it's just a huge mix of different perspectives, opinions and so on. Course you agree with some and you don't agree with others but that's half the fun, (like you were saying with the: "man, woman, punk, trendy, rich, poor").
As for this "club"...well I don't think there are any reasonable grounds for stopping it (there definitely aren't legally..) and, to be honest, anyone who wants to be part of it who fits the "criteria" can and should be able to. It's not the kind of place I'd sign up to because I'd probably rather be at a pub (to be honest lol!!) with a few mates I've met here.