A very old climbing club - one of my old climbing partners was a member, and I've stayed at Tyn Twr, Dunmail ... and even Buckbarrow, when they had it - marvellous! But never Bishops Scale - too posh.
Although it is named after Pius XI, you don't have to be anything more than a keen mountaineer to join - although, from appearances, you do seem to have to be ... quite old!!