"You will be told to mind your own business and they would be right, as it would be the management's business to deal with this. "

well, whether the analogy is right or not, when there is a dispute among patrons/members, at some point it DOES fall to the management to deal with it, and no doubt someone will disagree with the decision. Management could ignore it and let the parties wrangle, or they could attempt to DO something. In this case, management chose to have a "no wrangling" section of the café, and those who choose BS 'noise' are now asked to take it down there ¬, with occasional sanctions for those who don't. (It is a pure judgement call whether those loud folks are making TOO much noise...how else can it be done?)

As I read the various threads where this issue is raised, it seems to me that management's decision is supported by something like 10-15 to 1.

As in restaurants where "no smoking" is now common, there are those who will NEVER be pleased, and will always feel they are being unfairly treated.