Looked at the site again and as I thought, It's a club for people who breed and show...in fairness, they don't really do anything that would interest most pet Chihuahua owners.
Having read the membership process, they only review memberships on occasion. They can do that because they are a specialist club. It seems events are organised around breeders rather than pet owners and I can understand that. Admin to have a section for us would no doubt be impractical?
Maybe you could start up a local group if there is none in your area for pet owners
I don't think they are being snobbish, simply being fair and not taking money from people when they have nothing really to offer them.