The line between reducing national identities to 1-2 syllables and using said syllables as a slur is a brittle and contextual one. The issues around "Jap" are deeply rooted in US/Japanese relations. It goes without saying that racism against Japan and
internment happened in Australia and New Zealand, too. But let's be realistic. America has 1.3 million Japanese people. Australia has 30,000. Australia and other countries didn't occupy Japan. DIdn't nuke Japan. Didn't humiliate the country and its citizens in such a direct way.
"Jap" is a very rare and unusual case. The whole Nipponese/Japanese thing has always been strange because we referred to the people of Nippon using a Chinese distortion of their name. The terms "Nip" and "Jap" arose naturally as shortened forms, without any malicious intent. (Any word that ends in "t" or "p" or similar sounds feels natural to say.) The stigmatization of "Jap" is rooted in American hate campaigns during WWII which were of great ferocity and bile followed by American bombing and occupying Japan. There's a reason the term quickly became taboo in American in particular. A perfectly normal word shortening -- the most logical and natural way of shortening the word that is going to recur over and over, especially in dialects of English that shorten words for the sake of it -- became taboo in America, and American influence spread this taboo.
Countries like Australia, the UK, and others had Japanese populations measured in the low thousands. For the average person, "Jap" ended up being applied to Japanese PRODUCTS, not Japanese individuals. Jap Cars, Jap Bikes, Jap Pumpkins. These terms are widely used today in Australia and NZ and find usage in various commonwealth countries. The extent to which they are used depends on how American-influenced your language is, basically.
The rise of the internet has made this kinda delicate. There are a lot of words and expressions that are completely benign in one language, one dialect, one culture, that are varying degrees of offensive in another. The internet is very US dominated. As a result, things that are offensive in the American context tend to be viewed as offensive on the internet at large.
In the interests of peace and civility online it is generally wise to try and use neutral terminology. If someone, somewhere is going to be offended by what you say, do think about saying it differently. For example, in British English, calling someone a fruitcake is normal. In American English it sometimes seen as offensive. But when I go to the store to buy a pumpkin for pumpkin soup, I am buying a Jap Pumpkin. That is its name. And there is zero racism attached to the name. When I need replacement parts for an old Japanese car, I go to JustJap, or JapParts. Those stores are so named because they sell parts for "Jap" cars.
Some people will try to equate this to "Abbo Auto" or something equally offensive. But calling a car from Japan a Jap car wasn't born of racism or derogatory sentiment. Importantly, it never gained such associations. Calling these (highly desirable) cars "Japanese Cars" was a mouthful. "Jap" was used because it's the first three letters of Japan.
The reason "Abbo" -- which was once a completely innocent expression -- is seen as a slur in the Australian context is because racism against indigenous Australians is alive and well today. It's an ongoing issue. We stole their land and ruined their future, and the least we can do for the time being is refer to them as "Aborigines", "Indigenous Australians", and "Koori", depending on formality. The context of words does matter. Where they are said. When they are said. At some point in the future when the native peoples of Australia are no longer an oppressed minority, perhaps "Abbo" will reenter polite society. For now it is taboo and people essentially demonstrate their consideration for the rightful owners of the country by declining to use it.
America's relationship with Japan is very unique because America mass-interned, bombed, and occupied them. There's a very specific context there that has tainted all informal words to describe the people of Japan. It's not just "Jap". There are zero polite nicknames for the inhabitants of countries the Americans stormed around in with their tanks. We have no polite nicknames for the Vietnamese. For the Koreans. For the various Arab countries. Everything is tainted by racism mixed with war. Using "Japan" as a full word is a form of respect for a country and a people that America did some very, very bad things to. Is this guilt projected onto the world at large? Yes. But the internet is a bad place for such nuances, and playing it safe is often best.