I say it should be kept open, but I agree with Samantha about some kind of magically binding contract being needed to assure secrecy before a member is accepted. Making a group totally exclusive would not only rob them of needed diversity, but it would probably drive away some people who they might really want/need to join the group, but would find the group to be too elite or snobbish once it was exclusive. Also, the Trio haven't exactly shown themselves to be the best judges of character, so how are they going to properly choose who will be loyal and is ok to join, and who isn't? And a binding magical contract would nullify any danger of a Slytherin or any other potential member ratting them out, so there would be no real need for exclusivity.
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