"It's quite correct that "Aussie" is not offensive. It's an affectionate term. And so is "Kiwi". And "Brit". "

I think if often depends on how the recipients of the word react to it. AFAIK the word "Brit" certainly on this side of the pond basically came in to use as a term used by Irish Republicans in what was meant to be a derogatory manner or at the very least certainly wasn't affectionate. Can anyone think of British people themselves, or others apart from the Irish, using the term before the 1970s and the "Brits Out" slogans etc? It just seems that the British themselves haven't regarded the word as offensive at all so therefore it isn't. Many people may prefer to be called English or Scottish etc to British (or being a Brit) but that is a different matter.